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Publisher: Springer-Verlag (Total: 2352 journals)

 Archiv der Mathematik   [SJR: 0.597]   [H-I: 29]   [1 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1420-8938 - ISSN (Online) 0003-889X    Published by Springer-Verlag  [2352 journals]
• Non-nudgable subgroups of permutations
• Authors: Tim Netzer
Pages: 401 - 406
Abstract: Abstract Motivated by a problem from behavioral economics, we study subgroups of permutation groups that have a certain strong symmetry. Given a fixed permutation, consider the set of all permutations with disjoint inversion sets. The group is called non-nudgable if the cardinality of this set always remains the same when replacing the initial permutation with its inverse. It is called nudgable otherwise. We show that all full permutation groups, standard dihedral groups, half of the alternating groups, and any abelian subgroup are non-nudgable. In the right probabilistic sense, it is thus quite likely that a randomly generated subgroup is non-nudgable. However, the other half of the alternating groups are nudgable. We also construct a smallest possible nudgable group, a 6-element subgroup of the permutation group on 4 elements.
PubDate: 2017-11-01
DOI: 10.1007/s00013-017-1086-4
Issue No: Vol. 109, No. 5 (2017)

• Metric ultraproducts of classical groups
• Authors: John S. Wilson
Pages: 407 - 412
Abstract: Abstract Simple non-discrete metric ultraproducts of classical groups are geodesic spaces with respect to a natural metric.
PubDate: 2017-11-01
DOI: 10.1007/s00013-017-1087-3
Issue No: Vol. 109, No. 5 (2017)

• Rings containing a field of characteristic zero
• Authors: David John Benson
Pages: 413 - 414
Abstract: Abstract Let K be a field of characteristic zero, and let R be a ring containing K. Then either $$R^\times = K^\times$$ or $$K^\times$$ is a subgroup of infinite index in $$R^\times$$ .
PubDate: 2017-11-01
DOI: 10.1007/s00013-017-1100-x
Issue No: Vol. 109, No. 5 (2017)

• Some results on the annihilators and attached primes of local cohomology
modules
• Authors: Ali Atazadeh; Monireh Sedghi; Reza Naghipour
Pages: 415 - 427
Abstract: Abstract Let $$(R, \mathfrak {m})$$ be a local ring and M a finitely generated R-module. It is shown that if M is relative Cohen–Macaulay with respect to an ideal $$\mathfrak {a}$$ of R, then $${\text {Ann}}_R(H_{\mathfrak {a}}^{{\text {cd}}(\mathfrak {a}, M)}(M))={\text {Ann}}_RM/L={\text {Ann}}_RM$$ and $${\text {Ass}}_R (R/{\text {Ann}}_RM)\subseteq \{\mathfrak {p}\in {\text {Ass}}_R M \,\mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})={\text {cd}}(\mathfrak {a}, M)\},$$ where L is the largest submodule of M such that $$\mathrm{cd}(\mathfrak {a}, L)< \mathrm{cd}(\mathfrak {a}, M)$$ . We also show that if $$H^{\dim M}_{\mathfrak {a}}(M)=0$$ , then $${\text {Att}}_R(H^{\dim M-1}_{\mathfrak {a}}(M))= \{\mathfrak {p}\in {\text {Supp}}(M) \mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})=\dim M-1\},$$ and so the attached primes of $$H^{\dim M-1}_{\mathfrak {a}}(M)$$ depend only on $${\text {Supp}}(M)$$ . Finally, we prove that if M is an arbitrary module (not necessarily finitely generated) over a Noetherian ring R with $$\mathrm{cd}(\mathfrak {a}, M)=\mathrm{cd}(\mathfrak {a}, R/{\text {Ann}}_RM)$$ , then $${\text {Att}}_R(H^{\mathrm{cd}(\mathfrak {a}, M)}_{\mathfrak {a}}(M))\subseteq \{\mathfrak {p}\in {\text {V}}({\text {Ann}}_RM) \,\mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})=\mathrm{cd}(\mathfrak {a}, M)\}.$$ As a consequence of this, it is shown that if $$\dim M=\dim R$$ , then $${\text {Att}}_R(H^{\dim M}_{\mathfrak {a}}(M))\subseteq \{\mathfrak {p}\in {\text {Ass}}_R M \mathrm{cd}(\mathfrak {a}, R/\mathfrak {p})=\dim M\}$$ .
PubDate: 2017-11-01
DOI: 10.1007/s00013-017-1081-9
Issue No: Vol. 109, No. 5 (2017)

• Energy integrals and small points for the Arakelov height
• Authors: Paul Fili; Clayton Petsche; Igor Pritsker
Pages: 441 - 454
Abstract: Abstract We study small points for the Arakelov height on the projective line. First, we identify the smallest positive value taken by the Arakelov height, and we characterize all cases of equality. Next we solve several archimedean energy minimization problems with respect to the chordal metric on the projective line, and as an application, we obtain lower bounds on the Arakelov height in fields of totally real and totally p-adic numbers.
PubDate: 2017-11-01
DOI: 10.1007/s00013-017-1080-x
Issue No: Vol. 109, No. 5 (2017)

• On the image, characterization, and automatic continuity of
$$\varvec{(\sigma }, \varvec{\tau }$$ ( σ , τ ) -derivations
• Authors: Amin Hosseini
Pages: 461 - 469
Abstract: Abstract The first main theorem of this paper asserts that any $$(\sigma , \tau )$$ -derivation d, under certain conditions, either is a $$\sigma$$ -derivation or is a scalar multiple of ( $$\sigma - \tau$$ ), i.e. $$d = \lambda (\sigma - \tau )$$ for some $$\lambda \in \mathbb {C} \backslash \{0\}$$ . By using this characterization, we achieve a result concerning the automatic continuity of $$(\sigma , \tau$$ )-derivations on Banach algebras which reads as follows. Let $$\mathcal {A}$$ be a unital, commutative, semi-simple Banach algebra, and let $$\sigma , \tau : \mathcal {A} \rightarrow \mathcal {A}$$ be two distinct endomorphisms such that $$\varphi \sigma (\mathbf e )$$ and $$\varphi \tau (\mathbf e )$$ are non-zero complex numbers for all $$\varphi \in \Phi _\mathcal {A}$$ . If $$d : \mathcal {A} \rightarrow \mathcal {A}$$ is a $$(\sigma , \tau )$$ -derivation such that $$\varphi d$$ is a non-zero linear functional for every $$\varphi \in \Phi _\mathcal {A}$$ , then d is automatically continuous. As another objective of this research, we prove that if $$\mathfrak {M}$$ is a commutative von Neumann algebra and $$\sigma :\mathfrak {M} \rightarrow \mathfrak {M}$$ is an endomorphism, then every Jordan $$\sigma$$ -derivation $$d:\mathfrak {M} \rightarrow \mathfrak {M}$$ is identically zero.
PubDate: 2017-11-01
DOI: 10.1007/s00013-017-1082-8
Issue No: Vol. 109, No. 5 (2017)

• On the reflexivity of $$\mathcal {P}_{w}(^{n}E;F)$$ P w ( n E ; F )
• Authors: Sergio A. Pérez
Pages: 471 - 475
Abstract: Abstract In this paper we prove that if E and F are reflexive Banach spaces and G is a closed linear subspace of the space $$\mathcal {L}_{K}(E;F)$$ of all compact linear operators from E into F, then G is either reflexive or non-isomorphic to a dual space. This result generalizes (Israel J Math 21:38-49, 1975, Theorem 2) and gives the solution to a problem posed by Feder (Ill J Math 24:196-205, 1980, Problem 1). We also prove that if E and F are reflexive Banach spaces, then the space $$\mathcal {P}_{w}(^{n}E;F)$$ of all n-homogeneous polynomials from E into F which are weakly continuous on bounded sets is either reflexive or non-isomorphic to a dual space.
PubDate: 2017-11-01
DOI: 10.1007/s00013-017-1084-6
Issue No: Vol. 109, No. 5 (2017)

• Endpoint estimates of positive operators in a filtered measure space
• Authors: Yahui Zuo; Lian Wu; Yong Jiao
Pages: 477 - 488
Abstract: Abstract In a filtered measure space, a necessary and sufficient Sawyer type condition is given under which a positive operator is bounded from $$L^1(d\mu )$$ to $$L^{q,\infty }(d\mu )$$ with $$1<q <\infty$$ . This result can be recognized as the endpoint case of Tanaka and Terasawa (Arch Math (Basel) 101:559–568, 2013, Theorem 1.1). We also establish a similar weak type inequality for generalized Doob’s maximal operators.
PubDate: 2017-11-01
DOI: 10.1007/s00013-017-1079-3
Issue No: Vol. 109, No. 5 (2017)

• On purely non-free finite actions of abelian groups on compact surfaces
• Authors: Czesław Bagiński; Grzegorz Gromadzki; Ruben A. Hidalgo
Pages: 311 - 321
Abstract: Abstract A finite group of self-homeomorphisms of a closed orientable surface is said to act on it purely non-freely if each of its elements has a fixed point; we also call it a gpnf-action. In this paper we observe that gpnf-actions exist for an arbitrary finite group and we discuss the minimum genus problem for such actions. We solve it for abelian groups. In the cyclic case we prove that the minimal gpnf-action genus coincides with Harvey’s minimal genus.
PubDate: 2017-10-01
DOI: 10.1007/s00013-017-1068-6
Issue No: Vol. 109, No. 4 (2017)

• Arithmetical rank of binomial ideals
• Authors: Anargyros Katsabekis
Pages: 323 - 334
Abstract: Abstract In this paper, we investigate the arithmetical rank of a binomial ideal J. We provide lower bounds for the binomial arithmetical rank and the J-complete arithmetical rank of J. Special attention is paid to the case where J is the binomial edge ideal of a graph. We compute the arithmetical rank of such an ideal in various cases.
PubDate: 2017-10-01
DOI: 10.1007/s00013-017-1071-y
Issue No: Vol. 109, No. 4 (2017)

• $$\varvec{L^p}$$ L p -norm estimate of the Bergman projection on Hartogs
triangle
• Authors: Tomasz Beberok
Pages: 341 - 353
Abstract: Abstract The purpose of this paper is to give an estimate of the $$L^p$$ -norm of the Bergman projection on the Hartogs triangle.
PubDate: 2017-10-01
DOI: 10.1007/s00013-017-1069-5
Issue No: Vol. 109, No. 4 (2017)

• L-weakly and M-weakly compact operators and the centre
• Authors: E. Bayram; A. W. Wickstead
Pages: 355 - 363
Abstract: Abstract We extend known results concerning the centre of spaces of regular (resp. weakly compact or compact) operators between two Banach lattices to the setting of L-weakly compact and M-weakly compact operators. We also show that the L-weakly compact, M-weakly compact, and compact operators lying in the centre of a Banach lattice coincide.
PubDate: 2017-10-01
DOI: 10.1007/s00013-017-1077-5
Issue No: Vol. 109, No. 4 (2017)

• A remainder term for Hölder’s inequality for matrices and
quantum entropy inequalities
• Authors: Eric A. Carlen
Pages: 365 - 371
Abstract: Abstract We prove a sharp remainder term for Hölder’s inequality for traces as a consequence of the uniform convexity properties of the Schatten trace norms. We then show how this implies a novel family of Pinsker type bounds for the quantum Rényi entropy. Finally, we show how the sharp form of the usual quantum Pinsker inequality for relative entropy may be obtained as a fairly direct consequence of uniform convexity.
PubDate: 2017-10-01
DOI: 10.1007/s00013-017-1066-8
Issue No: Vol. 109, No. 4 (2017)

• On g -functions for countable state subshifts
Pages: 373 - 381
Abstract: Abstract This note revisits the problem of finding necessary and sufficient conditions for a subshift to admit a continuous g-function. Results obtained by Krieger (in: IMS lecture notes monograph series, vol 48, pp 306–316, 2006) on finite alphabet subshifts are generalized to countable state subshifts.
PubDate: 2017-10-01
DOI: 10.1007/s00013-017-1063-y
Issue No: Vol. 109, No. 4 (2017)

• A gradient estimate on graphs with the $$\varvec{CDE(m,K)}$$ C D E ( m , K
) -condition
• Authors: Lin Feng Wang; Yu Jie Zhou
Pages: 383 - 391
Abstract: Abstract Let G(V, E) be an infinite (locally finite) graph. In this paper we prove that if G satisfies the $$CDE(m,-K)$$ -condition for some $$m>0,K\ge 0$$ , and $$u:V\rightarrow \mathbf {R}$$ is a positive solution to the following equation \begin{aligned} \triangle _{\mu } u=-\lambda u, \end{aligned} then $$\lambda \le \frac{mK}{2}$$ and u satisfies a gradient estimate, which is parallel to the results on complete noncompact Riemannian manifolds established by Li (Geometric analysis. Cambridge studies in advanced mathematics, Cambridge University Press, Cambridge, 2012), and on smooth metric measure spaces established by Wang (Ann Glob Anal Geom 37:393–402, 2010). As byproducts, we also get two Liouville theorems and a Harnack inequality.
PubDate: 2017-10-01
DOI: 10.1007/s00013-017-1078-4
Issue No: Vol. 109, No. 4 (2017)

• Localisation uniforme des espaces de Besov et de Lizorkin–Triebel
• Authors: Salah Eddine Allaoui; Gérard Bourdaud
Abstract: Résumé On établit des caractérisations intrinsèques des versions localisées-uniformes des espaces de Besov $${B_{{p},{q}}^{s}({\mathbb R}^n)}$$ , avec $$p,q\in [1,+\infty ]$$ , et de Lizorkin–Triebel $${F_{{p},{q}}^{s}({\mathbb R}^n)}$$ avec $$q\in [1,+\infty ]$$ et $$p\in [1,+\infty [$$ , quel que soit le nombre réel $$s>0$$ .
PubDate: 2017-10-03
DOI: 10.1007/s00013-017-1096-2

• Reduction of the Small Cohen–Macaulay Conjecture to excellent unique
factorization domains
• Authors: Ehsan Tavanfar
Abstract: Abstract In this article, applying the quasi-Gorenstein analogous of the Ulrich’s deformation of certain Gorenstein rings to unique factorization domains, we show that the Small Cohen–Macaulay Conjecture reduces to excellent unique factorization domains.
PubDate: 2017-09-22
DOI: 10.1007/s00013-017-1103-7

• Strict comparison theorems under sublinear expectations
• Authors: Xinpeng Li; Yiqing Lin
Abstract: Abstract In this paper, we consider strict comparison theorems in the framework of G-expectation, which is a type of sublinear expectation associated with fully nonlinear parabolic partial differential equations. In particular, we first apply Krylov–Safonov estimates to establish the strict comparison theorem for functions from the Lipschitz class $$Lip(\Omega )$$ . Then we prove generalized strict comparison theorems on the enlarged space $$L_G^1(\Omega )$$ , which is the Banach completion of $$Lip(\Omega )$$ under the G-expectation.
PubDate: 2017-09-22
DOI: 10.1007/s00013-017-1098-0

• Complex symmetry of Toeplitz operators with continuous symbols
• Authors: S. Waleed Noor
Abstract: Abstract In this note, we consider the question of when a Toeplitz operator on the Hardy–Hilbert space $$H^2$$ of the open unit disk $$\mathbb {D}$$ is complex symmetric, focusing on symbols $$\phi :\mathbb {T}\rightarrow \mathbb {C}$$ that are continuous on the unit circle $$\mathbb {T}=\partial \mathbb {D}$$ . A closed curve $$\phi$$ is called nowhere winding if the winding number of $$\phi$$ is 0 about every point not in the range of $$\phi$$ . It is then shown that if $$T_\phi$$ is complex symmetric, then $$\phi$$ must be nowhere winding. Hence if $$\phi$$ is a simple closed curve, then $$T_\phi$$ cannot be a complex symmetric operator. The spectrum and invertibility of complex symmetric Toeplitz operators with continuous symbols are then described. Finally, given any continuous curve $$\gamma :[a,b]\rightarrow \mathbb {C}$$ , it is shown that there exists a complex symmetric Toeplitz operator with continuous symbol whose spectrum is precisely the range of $$\gamma$$ .
PubDate: 2017-09-22
DOI: 10.1007/s00013-017-1101-9

• The prime-power hypothesis and solvable groups
• Authors: Ni Du; Mark L. Lewis
Abstract: Abstract We say that a group G satisfies the prime-power hypothesis if the GCDs for all pairs of distinct character degrees are prime powers. We prove that if G is a solvable group satisfying the prime-power hypothesis, then G has Fitting height at most 12. If in addition G is odd, then we prove that the Fitting height of G is at most 6.
PubDate: 2017-08-16
DOI: 10.1007/s00013-017-1085-5

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