scholarly journals On Homotopy Invariants of Tensor Products of Banach Algebras

2020 ◽  
Vol 92 (2) ◽  
Author(s):  
Alexander Brudnyi
Keyword(s):  
Banach Algebras ◽  
Tensor Products ◽  
Homotopy Invariants

scholarly journals Amenability of ultrapowers of Banach algebras

2009 ◽  
Vol 52 (2) ◽  
pp. 307-338 ◽  
Author(s):  
Matthew Daws
Keyword(s):  
Banach Space ◽  
Reflexive Banach Space ◽  
Banach Algebras ◽  
Tensor Products ◽  
Convolution Algebra ◽  
Abstract Characterization ◽  
Closed Subalgebra

AbstractWe study when certain properties of Banach algebras are stable under ultrapower constructions. In particular, we consider when every ultrapower of $\mathcal{A}$ is Arens regular, and give some evidence that this is so if and only if $\mathcal{A}$ is isomorphic to a closed subalgebra of operators on a super-reflexive Banach space. We show that such ideas are closely related to whether one can sensibly define an ultrapower of a dual Banach algebraffi We study how tensor products of ultrapowers behave, and apply this to study the question of when every ultrapower of $\mathcal{A}$ is amenable. We provide an abstract characterization in terms of something like an approximate diagonal, and consider when every ultrapower of a C*-algebra, or a group L1-convolution algebra, is amenable.

Tensor Products of Banach Algebras*

1968 ◽  
Vol 11 (5) ◽  
pp. 691-701
Author(s):  
Boaz Natzitz
Keyword(s):  
Tensor Product ◽  
Banach Algebras ◽  
Tensor Products ◽  
Group Algebras ◽  
Commutative Banach Algebras

In [3] Gelbaum defined the tensor product A ⊗CB of three commutative Banach algebras, A, B and C and established some of its properties. Various examples are given and the particular case where A, B and C are group algebras of L.C.A. groups G, H and K respectively, is discussed there. It is shown there that if K is compact L1(G) ⊗ L1(K) L1(H) is isomorphic to where is L.C.A. 1 L (K) 1 1 if and only if L1(G) ⊗ L1(K) L1(H) is semisimple.

scholarly journals Tensor products of Banach algebras. II

1970 ◽  
Vol 25 (3) ◽  
pp. 470-470 ◽  
Author(s):  
Bernard R. Gelbaum
Keyword(s):  
Banach Algebras ◽  
Tensor Products
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