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On the homological and algebraical properties of some Feichtinger algebras

  • Ali Rejali EMAIL logo and Navid Sabzali
Published/Copyright: October 4, 2021
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Abstract

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 Bmin 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 Bmin 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 Bmin is a symmetric Segal subalgebra of L1(G) on an IN-group G, under certain conditions, and we apply our results to study pseudo-amenability and some other homological properties of Bmin on IN-groups. Furthermore, we determine necessary and sufficient conditions on A under which Amin 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.

MSC 2010: 46H05; 46H25; 46J05; 46J20
  1. (Communicated by Emanuel Chetcuti)

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Received: 2020-05-16
Accepted: 2020-10-23
Published Online: 2021-10-04
Published in Print: 2021-10-26

© 2021 Mathematical Institute Slovak Academy of Sciences

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