Let A be a closed linear operator acting in a separable Hilbert space. Denote by co(A) the closed convex hull of the spectrum of A. An estimate for the norm of f(A) is obtained under the following conditions: f is a holomorphic function in a neighbourhood of co(A), and for some integer p the operator is Hilbert-Schmidt. The estimate improves one by I. Gelfand and G. Shilov.
@article{bwmeta1.element.bwnjournal-article-smv103i1p17bwm,
author = {M. Gil},
title = {On an estimate for the norm of a function of a quasihermitian operator},
journal = {Studia Mathematica},
volume = {103},
year = {1992},
pages = {17-24},
zbl = {0812.47014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv103i1p17bwm}
}
Gil, M. On an estimate for the norm of a function of a quasihermitian operator. Studia Mathematica, Tome 103 (1992) pp. 17-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv103i1p17bwm/
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