Translator Disclaimer
March 2020 Algebras of Diagonal Operators of the Form Scalar-Plus-Compact Are Calkin Algebras
Pavlos Motakis, Daniele Puglisi, Andreas Tolias
Michigan Math. J. 69(1): 97-152 (March 2020). DOI: 10.1307/mmj/1574845272

Abstract

For every Banach space X with a Schauder basis, consider the Banach algebra RIKdiag(X) of all diagonal operators that are of the form λI+K. We prove that RIKdiag(X) is a Calkin algebra, that is, there exists a Banach space YX such that the Calkin algebra of YX is isomorphic as a Banach algebra to RIKdiag(X). Among other applications of this theorem, we obtain that certain hereditarily indecomposable spaces and the James spaces Jp and their duals endowed with natural multiplications are Calkin algebras; that all nonreflexive Banach spaces with unconditional bases are isomorphic as Banach spaces to Calkin algebras; and that sums of reflexive spaces with unconditional bases with certain James–Tsirelson type spaces are isomorphic as Banach spaces to Calkin algebras.

Citation

Download Citation

Pavlos Motakis. Daniele Puglisi. Andreas Tolias. "Algebras of Diagonal Operators of the Form Scalar-Plus-Compact Are Calkin Algebras." Michigan Math. J. 69 (1) 97 - 152, March 2020. https://doi.org/10.1307/mmj/1574845272

Information

Received: 15 January 2018; Revised: 8 February 2018; Published: March 2020
First available in Project Euclid: 27 November 2019

zbMATH: 07208927
MathSciNet: MR4071347
Digital Object Identifier: 10.1307/mmj/1574845272

Subjects:
Primary: 46B03, 46B25, 46B28, 46B45

Rights: Copyright © 2020 The University of Michigan

JOURNAL ARTICLE
56 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.69 • No. 1 • March 2020
Back to Top