Calkin algebras for Banach spaces with finitely decomposable quotients

Manuel González, and José M. Herrera. "Calkin algebras for Banach spaces with finitely decomposable quotients." Studia Mathematica 157.3 (2003): 279-293. <http://eudml.org/doc/285318>.

@article{ManuelGonzález2003,
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 × 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.},
author = {Manuel González, José M. Herrera},
journal = {Studia Mathematica},
keywords = {Calkin algebras; Banach spaces; algebra isomorphisms},
language = {eng},
number = {3},
pages = {279-293},
title = {Calkin algebras for Banach spaces with finitely decomposable quotients},
url = {http://eudml.org/doc/285318},
volume = {157},
year = {2003},
}

TY - JOUR
AU - Manuel González
AU - José M. Herrera
TI - Calkin algebras for Banach spaces with finitely decomposable quotients
JO - Studia Mathematica
PY - 2003
VL - 157
IS - 3
SP - 279
EP - 293
AB - 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.
LA - eng
KW - Calkin algebras; Banach spaces; algebra isomorphisms
UR - http://eudml.org/doc/285318
ER -