Calkin algebras for Banach spaces with finitely decomposable quotients

• Autorzy: Manuel González , José M. Herrera
• Języki publikacji: EN

Abstrakty

EN

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 × 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 × 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.

Kategorie tematyczne

• 47A53: (Semi-) Fredholm operators; index theories
• 46B20: Geometry and structure of normed linear spaces
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 157
• Numer: 3
• Strony: 279-293

Daty

wydano

2003

Twórcy

autor

Manuel González

• Departamento de Matemáticas, Universidad de Cantabria, E-39071 Santander, Spain

autor

José M. Herrera

• Departamento de Matemáticas, Universidad de Cantabria, E-39071 Santander, Spain

Identyfikatory

DOI

10.4064/sm157-3-3