Calkin algebras for Banach spaces with finitely
 decomposable quotients

Manuel González; José M. Herrera

doi:10.4064/sm157-3-3

Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Studia Mathematica / All issues

Calkin algebras for Banach spaces with finitely decomposable quotients

Volume 157 / 2003

Manuel González, José M. Herrera Studia Mathematica 157 (2003), 279-293 MSC: Primary 47A10, 47A53; Secondary 46B20. DOI: 10.4064/sm157-3-3

Abstract

For a Banach space $X$ such that all quotients only admit direct decompositions with a number of summands smaller than or equal to $n$ , we show that every operator $T$ on $X$ can be identified with an $n\times n$ scalar matrix modulo the strictly cosingular operators $SC(X)$ . More precisely, we obtain an algebra isomorphism from the Calkin algebra $L(X)/SC(X)$ onto a subalgebra of the algebra of $n\times n$ scalar matrices which is triangularizable when $X$ is indecomposable. From this fact we get some information on the class of all semi-Fredholm operators on $X$ and on the essential spectrum of an operator acting on $X$ .

Authors

Manuel GonzálezDepartamento de Matemáticas
Universidad de Cantabria
E-39071 Santander, Spain
e-mail
José M. HerreraDepartamento de Matemáticas
Universidad de Cantabria
E-39071 Santander, Spain
e-mail

Free download under CC-BY license

Search for IMPAN publications