Abstract
For every Banach space with a Schauder basis, consider the Banach algebra of all diagonal operators that are of the form . We prove that is a Calkin algebra, that is, there exists a Banach space such that the Calkin algebra of is isomorphic as a Banach algebra to . Among other applications of this theorem, we obtain that certain hereditarily indecomposable spaces and the James spaces 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
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
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