# Perturbations of the H∞-calculus

Collectanea Mathematica (2007)

• Volume: 58, Issue: 3, page 291-325
• ISSN: 0010-0757

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## Abstract

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Suppose A is a sectorial operator on a Banach space X, which admits an H∞-calculus. We study conditions on a multiplicative perturbation B of A which ensure that B also has an H∞-calculus. We identify a class of bounded operators T : X→X, which we call strongly triangular, such that if B = (1 + T) A is sectorial then it also has an H∞-calculus. In the case X is a Hilbert space an operator is strongly triangular if and only if ∑ Sn(T)/n &lt;∞ where (Sn(T))n=1∞ are the singular values of T.

## How to cite

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Kalton, N.J.. "Perturbations of the H∞-calculus." Collectanea Mathematica 58.3 (2007): 291-325. <http://eudml.org/doc/42036>.

@article{Kalton2007,
abstract = {Suppose A is a sectorial operator on a Banach space X, which admits an H∞-calculus. We study conditions on a multiplicative perturbation B of A which ensure that B also has an H∞-calculus. We identify a class of bounded operators T : X→X, which we call strongly triangular, such that if B = (1 + T) A is sectorial then it also has an H∞-calculus. In the case X is a Hilbert space an operator is strongly triangular if and only if ∑ Sn(T)/n &lt;∞ where (Sn(T))n=1∞ are the singular values of T. },
author = {Kalton, N.J.},
journal = {Collectanea Mathematica},
keywords = {functional calculus; sectorial operator; operator ideal},
language = {eng},
number = {3},
pages = {291-325},
title = {Perturbations of the H∞-calculus},
url = {http://eudml.org/doc/42036},
volume = {58},
year = {2007},
}

TY - JOUR
AU - Kalton, N.J.
TI - Perturbations of the H∞-calculus
JO - Collectanea Mathematica
PY - 2007
VL - 58
IS - 3
SP - 291
EP - 325
AB - Suppose A is a sectorial operator on a Banach space X, which admits an H∞-calculus. We study conditions on a multiplicative perturbation B of A which ensure that B also has an H∞-calculus. We identify a class of bounded operators T : X→X, which we call strongly triangular, such that if B = (1 + T) A is sectorial then it also has an H∞-calculus. In the case X is a Hilbert space an operator is strongly triangular if and only if ∑ Sn(T)/n &lt;∞ where (Sn(T))n=1∞ are the singular values of T.
LA - eng
KW - functional calculus; sectorial operator; operator ideal
UR - http://eudml.org/doc/42036
ER -

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