[Banach] Abstract of a paper by Pavlos Motakis, Daniele Puglisi and Despoina Zisimopoulou

This is an announcement for the paper "A hierarchy of separable commutative Calkin algebras" by Pavlos Motakis, Daniele Puglisi and Despoina Zisimopoulou.

Abstract: For specific well founded countably branching trees $\mathcal{T}$ we construct $\mathcal{L}_\infty$ spaces $X_{\mathcal{T}}$. For each such tree $\mathcal{T}$ the Calkin algebra of $X_{\mathcal{T}}$ strongly resembles $C(\mathcal{T})$, the algebra of continuous functions defined on $\mathcal{T}$ and in the case in which $\mathcal{T}$ has finite height, those two algebras are homomorphic. We conclude that for every countable compact metric space $K$ with finite Cantor-Bendixson index there exists a $\mathcal{L}_\infty$ space whose Calkin algebra is isomorphic, as a Banach algebra, to $C(K)$.

Archive classification: math.FA

Mathematics Subject Classification: 46B03, 46B25, 46B28

Remarks: 28 pages

Submitted from: pmotakis@central.ntua.gr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1407.8073

or

http://arXiv.org/abs/1407.8073