|
Journal of the Australian Mathematical Society
Journal Prestige (SJR): 0.46  Citation Impact (citeScore): 1 Number of Followers: 0  Subscription journalISSN (Print) 1446-7887 - ISSN (Online) 1446-8107 Published by Cambridge University Press  [374 journals]
|
- JAZ volume 107 Issue 2 Cover and Front matter
- PubDate: 2019-10-01T00:00:00.000Z
DOI: 10.1017/S144678871800054X
Issue No: Vol. 107, No. 2 (2019)
- PubDate: 2019-10-01T00:00:00.000Z
- JAZ volume 107 Issue 2 Cover and Back matter
- PubDate: 2019-10-01T00:00:00.000Z
DOI: 10.1017/S1446788718000551
Issue No: Vol. 107, No. 2 (2019)
- PubDate: 2019-10-01T00:00:00.000Z
- Authors: IAIN FORSYTH; ADAM RENNIE
Pages: 145 - 180
Abstract: We provide sufficient conditions to factorise an equivariant spectral triple as a Kasparov product of unbounded classes constructed from the group action on the algebra and from the fixed point spectral triple. We show that if factorisation occurs, then the equivariant index of the spectral triple vanishes. Our results are for the action of compact abelian Lie groups, and we demonstrate them with examples from manifolds and
$\unicode[STIX]{x1D703}$ -deformations. In particular, we show that equivariant Dirac-type spectral triples on the total space of a torus principal bundle always factorise. Combining this with our index result yields a special case of the Atiyah–Hirzebruch theorem. We also present an example that shows what goes wrong in the absence of our sufficient conditions (and how we get around it for this example).
PubDate: 2019-10-01T00:00:00.000Z
DOI: 10.1017/S1446788718000423
Issue No: Vol. 107, No. 2 (2019)
- Authors: IAIN FORSYTH; ADAM RENNIE
- AC-GORENSTEIN RINGS AND THEIR STABLE MODULE CATEGORIES
- Authors: JAMES GILLESPIE
Pages: 181 - 198
Abstract: We introduce what is meant by an AC-Gorenstein ring. It is a generalized notion of Gorenstein ring that is compatible with the Gorenstein AC-injective and Gorenstein AC-projective modules of Bravo–Gillespie–Hovey. It is also compatible with the notion of
$n$ -coherent rings introduced by Bravo–Perez. So a 
$0$ -coherent AC-Gorenstein ring is precisely a usual Gorenstein ring in the sense of Iwanaga, while a 
$1$ -coherent AC-Gorenstein ring is precisely a Ding–Chen ring. We show that any AC-Gorenstein ring admits a stable module category that is compactly generated and is the homotopy category of two Quillen equivalent abelian model category structures. One is projective with cofibrant objects that are Gorenstein AC-projective modules while the other is an injective model structure with fibrant objects that are Gorenstein AC-injectives.
PubDate: 2019-10-01T00:00:00.000Z
DOI: 10.1017/S1446788718000290
Issue No: Vol. 107, No. 2 (2019)
- Authors: JAMES GILLESPIE
- SPECTRA OF LINEAR FRACTIONAL COMPOSITION OPERATORS ON THE GROWTH SPACE AND
BLOCH SPACE OF THE UPPER HALF-PLANE- Authors: SHI-AN HAN; ZE-HUA ZHOU
Pages: 199 - 214
Abstract: In this article, we provide a complete description of the spectra of linear fractional composition operators acting on the growth space and Bloch space over the upper half-plane. In addition, we also prove that the norm, essential norm, spectral radius and essential spectral radius of a composition operator acting on the growth space are all equal.
PubDate: 2019-10-01T00:00:00.000Z
DOI: 10.1017/S1446788718000289
Issue No: Vol. 107, No. 2 (2019)
- Authors: SHI-AN HAN; ZE-HUA ZHOU
- INFINITELY MANY SOLUTIONS FOR NONLOCAL SYSTEMS INVOLVING FRACTIONAL
LAPLACIAN UNDER NONCOMPACT SETTINGS- Authors: M. KHIDDI; S. BENMOULOUD, S. M. SBAI
Pages: 215 - 233
Abstract: In this paper, we study a class of Brezis–Nirenberg problems for nonlocal systems, involving the fractional Laplacian
$(-\unicode[STIX]{x1D6E5})^{s}$ operator, for 
$0
PubDate: 2019-10-01T00:00:00.000Z
DOI: 10.1017/S1446788718000307
Issue No: Vol. 107, No. 2 (2019)
- Authors: M. KHIDDI; S. BENMOULOUD, S. M. SBAI
- CONTACT METRIC THREE-MANIFOLDS WITH CONSTANT SCALAR TORSION
- Authors: T. KOUFOGIORGOS; C. TSICHLIAS
Pages: 234 - 255
Abstract: In this paper we study three-dimensional contact metric manifolds satisfying
$\Vert \unicode[STIX]{x1D70F}\Vert =\text{constant}$ . The local description, as well as several global results and new examples of such manifolds are given.
PubDate: 2019-10-01T00:00:00.000Z
DOI: 10.1017/S1446788718000265
Issue No: Vol. 107, No. 2 (2019)
- Authors: T. KOUFOGIORGOS; C. TSICHLIAS
- CLASSICAL PROPERTIES OF COMPOSITION OPERATORS ON HARDY–ORLICZ SPACES
ON PLANAR DOMAINS- Authors: MICHAŁ RZECZKOWSKI
Pages: 256 - 271
Abstract: In this paper we study composition operators on Hardy–Orlicz spaces on multiply connected domains whose boundaries consist of finitely many disjoint analytic Jordan curves. We obtain a characterization of order-bounded composition operators. We also investigate weak compactness and the Dunford–Pettis property of these operators.
PubDate: 2019-10-01T00:00:00.000Z
DOI: 10.1017/S1446788718000277
Issue No: Vol. 107, No. 2 (2019)
- Authors: MICHAŁ RZECZKOWSKI
- GENERALIZED CONTINUED FRACTION EXPANSIONS WITH CONSTANT PARTIAL
DENOMINATORS- Authors: TOPI TÖRMÄ
Pages: 272 - 288
Abstract: We study generalized continued fraction expansions of the form
$$\begin{eqnarray}\frac{a_{1}}{N}\frac{}{+}\frac{a_{2}}{N}\frac{}{+}\frac{a_{3}}{N}\frac{}{+}\frac{}{\cdots },\end{eqnarray}$$ where 
$N$ is a fixed positive integer and the partial numerators 
$a_{i}$ are positive integers for all 
$i$ . We call these expansions 
$\operatorname{dn}_{N}$ expansions and show that every positive real number has infinitely many 
$\operatorname{dn}_{N}$ expansions for each 
$N$ . In particular, we study the 
$\operatorname{dn}_{N}$ expansions of rational numbers and quadratic irrationals. Finally, we show that every positive real number has, for each 
$N$ , a 
$\operatorname{dn}_{N}$ expansion with bounded partial numerators.
PubDate: 2019-10-01T00:00:00.000Z
DOI: 10.1017/S1446788718000332
Issue No: Vol. 107, No. 2 (2019)
- Authors: TOPI TÖRMÄ
