Two well-known theorems for Hermitian elements in C*-algebras are extended to Banach algebras. The first concerns the solution of the equation ax - xb = y, and the second gives sharp bounds for the distance between spectra of a and b when a, b are Hermitian.
@article{bwmeta1.element.bwnjournal-article-smv134i2p111bwm,
author = {Rajendra Bhatia and Driss Drissi},
title = {Perturbation theorems for Hermitian elements in Banach algebras},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {111-117},
zbl = {0940.46026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv134i2p111bwm}
}
Bhatia, Rajendra; Drissi, Driss. Perturbation theorems for Hermitian elements in Banach algebras. Studia Mathematica, Tome 133 (1999) pp. 111-117. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv134i2p111bwm/
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