# Perturbations of the H∞-calculus

Collectanea Mathematica (2007)

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

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topKalton, 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 <∞ 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 <∞ 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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