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 Annales Universitatis Mariae Curie-Sklodowska, sectio A – MathematicaNumber of Followers: 1     Open Access journal ISSN (Print) 0365-1029 - ISSN (Online) 2083-7402 Published by Wydawnictwo UMCS  [25 journals]
• Upper and lower bounds for an integral transform of positive operators in
Hilbert spaces with applications

• Authors: Silvestru Sever Dragomir
Pages: 1 - 15
Abstract: For a continuous and positive function $$w(\lambda)$$, $$\lambda>0$$ and a positive measure $$\mu$$ on $$(0,\infty )$$ we consider the following integral transform
$\mathcal{D}( w,\mu ) ( T) :=\int_{0}^{\infty }w(\lambda) (\lambda +T)^{-1} d\mu ( \lambda ) ,$
where the integral is assumed to exist for any positive operator $$T$$ on a complex Hilbert space $$H$$. In this paper we obtain several upper and lower bounds for the difference $$\mathcal{D}( w,\mu ) ( A) -\mathcal{D}( w,\mu ) ( B)$$ under certain assumptions for the operators $$A$$ and $$B$$. Some natural applications for operator monotone and operator convex functions are also given.
PubDate: 2022-10-05
DOI: 10.17951/a.2022.76.1.1-15
Issue No: Vol. 76, No. 1 (2022)

• Bell numbers and Kurepa’s conjecture

• Authors: Luis Gallardo
Pages: 17 - 23
Abstract: We prove under a mild condition that Kurepa's conjecture holds for the set of prime numbers $$p$$ such that $$(\frac{p-1}{2})! = {2 \overwithdelims () p\;}$$ in $$\mathbb{F}_p$$.
PubDate: 2022-10-05
DOI: 10.17951/a.2022.76.1.17-23
Issue No: Vol. 76, No. 1 (2022)

• A note on the Banach–Mazur distances between $$c_0$$ and other
$$\ell_1$$-preduals

• Authors: Agnieszka Gergont
Pages: 25 - 30
Abstract: We prove that if $$X$$ is an $$\ell_{1}$$-predual isomorphic to the space $$c_{0}$$ of sequences converging to zero, then for any isomorphism $$T:X\rightarrow c_{0}$$ we have $$\Vert T\Vert\, \Vert T^{-1}\Vert\ge1+2r^{*}(X)$$, where $$r^{*}(X)$$ is the smallest radius of the closed ball of the dual space $$X^{*}$$ containing  all the weak$$^{*}$$ cluster points of the set of all extreme points of the closed unit ball of  $$X^*$$.
PubDate: 2022-10-05
DOI: 10.17951/a.2022.76.1.25-30
Issue No: Vol. 76, No. 1 (2022)

• The twisted gauge-natural bilinear brackets on couples of linear vector
fields and linear p-forms

• Authors: Jan Kurek, Włodzimierz Mikulski
Pages: 31 - 46
Abstract: We completely describe all gauge-natural operators $$C$$ which send linear $$(p+2)$$-forms $$H$$ on vector bundles $$E$$ (with sufficiently large dimensional bases) into $$\mathbf{R}$$-bilinear operators $$C_H$$ transforming pairs $$(X_1\oplus\omega_1,X_2\oplus\omega_2)$$ of couples of linear vector fields and linear $$p$$-forms on $$E$$ into couples $$C_H(X_1\oplus\omega_1, X_2\oplus\omega_2)$$ of linear vector fields and linear $$p$$-forms on $$E$$. Further, we extract all $$C$$ (as above) such that $$C_0$$ is the restriction of the well-known Courant bracket and $$C_H$$ satisfies the Jacobi identity in Leibniz form for all closed linear $$(p+2)$$-forms $$H$$.
PubDate: 2022-10-05
DOI: 10.17951/a.2022.76.1.31-46
Issue No: Vol. 76, No. 1 (2022)

• Matrix representations of third order jet groups

• Authors: Dusan Navratil
Pages: 47 - 59
Abstract: In this paper, faithful matrix representations of the jet groups $$G^3_n$$ are presented, following a detailed description of their components in block form. Such  groups can be used further to study symmetries of differential equations. Elements of these matrix representations are derived.
PubDate: 2022-10-05
DOI: 10.17951/a.2022.76.1.47-59
Issue No: Vol. 76, No. 1 (2022)

• A new characterization of strict convexity on normed linear spaces

• Authors: Nermin Okicic, Amra Rekic-Vukovic, Vedad Pasic
Pages: 61 - 71
Abstract: We consider relations between the distance of a set $$A$$ and the distance of its translated set $$A+x$$ from 0, for $$x\in A$$, in a normed linear space. If the relation $$d(0,A+x)<d(0,A)+\ x\$$ holds for exactly determined vectors $$x\in A$$, where $$A$$ is a convex, closed set with positive distance from 0, which we call (TP) property, then this property is equivalent to strict convexity of the space. We show that in uniformly convex spaces the considered property holds.
PubDate: 2022-10-05
DOI: 10.17951/a.2022.76.1.61-71
Issue No: Vol. 76, No. 1 (2022)

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