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SOME HOMOLOGICAL PROPERTIES OF FOURIER ALGEBRAS ON HOMOGENEOUS SPACES

Part of: Selfadjoint operator algebras Abstract harmonic analysis

Published online by Cambridge University Press:  09 November 2020

REZA ESMAILVANDI  and
MEHDI NEMATI
REZA ESMAILVANDI
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan84156-83111, Iran e-mail: r.esmailvandi@math.iut.ac.ir
MEHDI NEMATI*
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan84156-83111, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, P.O. Box: 19395–5746, Iran
*
e-mail: m.nemati@iut.ac.ir
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Abstract

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Let $ H $ be a compact subgroup of a locally compact group $ G $ . We first investigate some (operator) (co)homological properties of the Fourier algebra $A(G/H)$ of the homogeneous space $G/H$ such as (operator) approximate biprojectivity and pseudo-contractibility. In particular, we show that $ A(G/H) $ is operator approximately biprojective if and only if $ G/H $ is discrete. We also show that $A(G/H)^{**}$ is boundedly approximately amenable if and only if G is compact and H is open. Finally, we consider the question of existence of weakly compact multipliers on $A(G/H)$ .

Keywords

Fourier algebrahomogeneous spacehomological propertyweakly compact multiplier

MSC classification

Primary: 43A85: Analysis on homogeneous spaces
Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 46L07: Operator spaces and completely bounded maps
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 1 , August 2021 , pp. 132 - 140
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

Footnotes

This research for the second author was in part supported by a grant from IPM (no. 99170411).

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