# Pointwise multiplication operators on weighted Banach spaces of analytic functions

J. Bonet; P. Domański; M. Lindström

Studia Mathematica (1999)

- Volume: 137, Issue: 2, page 177-194
- ISSN: 0039-3223

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topBonet, J., Domański, P., and Lindström, M.. "Pointwise multiplication operators on weighted Banach spaces of analytic functions." Studia Mathematica 137.2 (1999): 177-194. <http://eudml.org/doc/216683>.

@article{Bonet1999,

abstract = {For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator $M_φ$, $M_φ(f)=φf$, on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when $M^\{\prime \}_φ$ is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map $M^\{\prime \}_φ$.},

author = {Bonet, J., Domański, P., Lindström, M.},

journal = {Studia Mathematica},

keywords = {weighted Banach spaces of analytic functions; pointwise multiplication operator; essential norm, closed range; approximative point spectrum; maximal ideal space of $H^∞$; Shilov boundary; Gleason part; hypercyclic operator; chaotic operator; hyperbolic operator; closed range operator; weighted Banach space; multplication operator; maximal ideal space},

language = {eng},

number = {2},

pages = {177-194},

title = {Pointwise multiplication operators on weighted Banach spaces of analytic functions},

url = {http://eudml.org/doc/216683},

volume = {137},

year = {1999},

}

TY - JOUR

AU - Bonet, J.

AU - Domański, P.

AU - Lindström, M.

TI - Pointwise multiplication operators on weighted Banach spaces of analytic functions

JO - Studia Mathematica

PY - 1999

VL - 137

IS - 2

SP - 177

EP - 194

AB - For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator $M_φ$, $M_φ(f)=φf$, on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when $M^{\prime }_φ$ is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map $M^{\prime }_φ$.

LA - eng

KW - weighted Banach spaces of analytic functions; pointwise multiplication operator; essential norm, closed range; approximative point spectrum; maximal ideal space of $H^∞$; Shilov boundary; Gleason part; hypercyclic operator; chaotic operator; hyperbolic operator; closed range operator; weighted Banach space; multplication operator; maximal ideal space

UR - http://eudml.org/doc/216683

ER -

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