Amenability and Super-amenability of Some Feichtinger Algebras

Rejali, Ali; Sabzali, Navid

doi:10.1007/s40995-020-00907-2

Iran J Sci Technol Trans Sci

2020

DOI: 10.1007/s40995-020-00907-2

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Amenability and Super-amenability of Some Feichtinger Algebras

Ali Rejali

Navid Sabzali

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2021

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On the homological and algebraical properties of some Feichtinger algebras

Rejali

Sabzali

2021

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Let G be a locally compact group (not necessarily abelian) and B be a homogeneous Banach space on G, which is in a good situation with respect to a homogeneous function algebra on G. Feichtinger showed that there exists a minimal Banach space B min in the family of all homogenous Banach spaces C on G, containing all elements of B with compact support. In this paper, the amenability and super amenability of B min with respect to the convolution product or with respect to the pointwise product are showed to correspond to amenability, discreteness or finiteness of the group G and conversely. We also prove among other things that B min is a symmetric Segal subalgebra of L 1(G) on an IN-group G, under certain conditions, and we apply our results to study pseudo-amenability and some other homological properties of B min on IN-groups. Furthermore, we determine necessary and sufficient conditions on A under which A min $\mathcal{A}_{\min}$ with the pointwise product is an abstract Segal algebra or Segal algebra in A, whenever A is a homogeneous function algebra with an approximate identity. We apply these results to study amenability of some Feichtinger algebras with respect to the pointwise product.

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On the homological and algebraical properties of some Feichtinger algebras

Rejali

Sabzali

2021

Mathematica Slovaca

View full text Add to dashboard Cite

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Amenability and Super-amenability of Some Feichtinger Algebras

Cited by 1 publication

References 22 publications

On the homological and algebraical properties of some Feichtinger algebras

On the homological and algebraical properties of some Feichtinger algebras

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