Amenability of ultrapowers of Banach algebras
نویسنده
چکیده
We study when certain properties of Banach algebras are stable under ultrapower constructions. In particular, we consider when every ultrapower of A is Arens regular, and give some evidence that this is so if and only if 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 algebra. We study how tensor products of ultrapowers behave, and apply this to study the question of when every ultrapower of A is amenable. We provide an abstract characterisation in terms of something like an approximate diagonal, and consider when every ultrapower of a C-algebra, or a group L-convolution algebra, is amenable. 2000 Mathematics Subject Classification: Primary 46B08, 46B28, 46H05, 43A20; Secondary 22D15, 47L10, 46M05, 46M07
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