Banach space properties forcing a reflexive amenable Banach algebra to be trivial

Details Banach space properties forcing a reflexive amenable Banach algebra to be trivial Banach space properties forcing a reflexive amenable Banach algebra to be trivial

2002-03-19

arxiv.org/abs/math/0203197v1

Arch. Math. (Basel) 77 (2001), 265-272

Mathematics

Functional Analysis

10 pages

Scientific paper

It is an open problem whether an infinite-dimensional amenable Banach algebra exists whose underlying Banach space is reflexive. We give sufficient conditions for a reflexive, amenable Banach algebra to be finite-dimensional (and thus a finite direct sum of full matrix algebras). If $A$ is a reflexive, amenable Banach algebra such that for each maximal left ideal $L$ of $A$ (i) the quotient $A / L$ has the approximation property and (ii) the canonical map from $A \check{\otimes} L^\perp$ to $(A / L) \wtensor L^\perp$ is open, then $A$ is finite-dimensional. As an application, we show that, if $A$ is an a menable Banach algebra whose underlying Banach space is an ${\cal L}^p$-space with $p \in (1,\infty)$ such that for each maximal left ideal $L$ the quotient $A / L$ has the approximation property, then $A$ is finite-dimensional.

Affiliated with

Also associated with

No associations

Rating

Banach space properties forcing a reflexive amenable Banach algebra to be trivial does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Banach space properties forcing a reflexive amenable Banach algebra to be trivial, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Banach space properties forcing a reflexive amenable Banach algebra to be trivial will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-620460