Banach space properties forcing a reflexive amenable Banach algebra to be trivial
| dc.creator | Runde, Volker | |
| dc.date | 2002-03-19 | |
| dc.date.accessioned | 2026-07-07T04:47:10Z | |
| dc.date.available | 2026-07-07T04:47:10Z | |
| dc.description | 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. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0203197 | |
| dc.identifier | http://arxiv.org/abs/math/0203197 | |
| dc.identifier | Arch. Math. (Basel) 77 (2001), 265-272 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63606 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B10, 46B20, 46H20 (primary), 46H25, 46M18 | |
| dc.title | Banach space properties forcing a reflexive amenable Banach algebra to be trivial | |
| dc.type | text |