Michigan Mathematical Journal
- Michigan Math. J.
- Volume 69, Issue 1 (2020), 97-152.
Algebras of Diagonal Operators of the Form Scalar-Plus-Compact Are Calkin Algebras
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.
Michigan Math. J., Volume 69, Issue 1 (2020), 97-152.
Received: 15 January 2018
Revised: 8 February 2018
First available in Project Euclid: 27 November 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46B03: Isomorphic theory (including renorming) of Banach spaces 46B25: Classical Banach spaces in the general theory 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 46B45: Banach sequence spaces [See also 46A45]
Motakis, Pavlos; Puglisi, Daniele; Tolias, Andreas. Algebras of Diagonal Operators of the Form Scalar-Plus-Compact Are Calkin Algebras. Michigan Math. J. 69 (2020), no. 1, 97--152. doi:10.1307/mmj/1574845272. https://projecteuclid.org/euclid.mmj/1574845272