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

Abstract

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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 ) = φ f , on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when M φ ' is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map M φ ' .

How to cite

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Bonet, 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 -

References

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