The algebra generated by a pair of operator weighted shifts

Marek Ptak

Annales Polonici Mathematici (1995)

  • Volume: 62, Issue: 2, page 97-110
  • ISSN: 0066-2216

Abstract

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We present a model for two doubly commuting operator weighted shifts. We also investigate general pairs of operator weighted shifts. The above model generalizes the model for two doubly commuting shifts. WOT-closed algebras for such pairs are described. We also deal with reflexivity for such pairs assuming invertibility of operator weights and a condition on the joint point spectrum.

How to cite

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Marek Ptak. "The algebra generated by a pair of operator weighted shifts." Annales Polonici Mathematici 62.2 (1995): 97-110. <http://eudml.org/doc/262673>.

@article{MarekPtak1995,
abstract = {We present a model for two doubly commuting operator weighted shifts. We also investigate general pairs of operator weighted shifts. The above model generalizes the model for two doubly commuting shifts. WOT-closed algebras for such pairs are described. We also deal with reflexivity for such pairs assuming invertibility of operator weights and a condition on the joint point spectrum.},
author = {Marek Ptak},
journal = {Annales Polonici Mathematici},
keywords = {pairs of operator weighted shifts; reflexive algebras; doubly commuting operator weighted shifts; WOT-closed algebras; invertibility of operator weights; joint point spectrum},
language = {eng},
number = {2},
pages = {97-110},
title = {The algebra generated by a pair of operator weighted shifts},
url = {http://eudml.org/doc/262673},
volume = {62},
year = {1995},
}

TY - JOUR
AU - Marek Ptak
TI - The algebra generated by a pair of operator weighted shifts
JO - Annales Polonici Mathematici
PY - 1995
VL - 62
IS - 2
SP - 97
EP - 110
AB - We present a model for two doubly commuting operator weighted shifts. We also investigate general pairs of operator weighted shifts. The above model generalizes the model for two doubly commuting shifts. WOT-closed algebras for such pairs are described. We also deal with reflexivity for such pairs assuming invertibility of operator weights and a condition on the joint point spectrum.
LA - eng
KW - pairs of operator weighted shifts; reflexive algebras; doubly commuting operator weighted shifts; WOT-closed algebras; invertibility of operator weights; joint point spectrum
UR - http://eudml.org/doc/262673
ER -

References

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  1. [1] N. P. Jawell and A. R. Lubin, Commuting weighted shifts and analytic function theory in several variables, J. Operator Theory 1 (1979), 207-223. Zbl0431.47016
  2. [2] A. Lambert, The algebra generated by an invertibly weighted shift, J. London Math. Soc. (2) 5 (1972), 741-747. Zbl0244.46079
  3. [3] A. Lambert, Unitary equivalence and reducibility of invertibly weighted shifts, Bull. Austral. Math. Soc. 5 (1971), 157-173. Zbl0217.45303
  4. [4] M. Ptak, Reflexivity of pairs of shifts, Proc. Amer. Math. Soc. 109 (1990), 409-415. Zbl0734.47023
  5. [5] A. L. Shields and L. J. Wallen, The commutant of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971), 777-788. Zbl0207.13801
  6. [6] M. Słociński, On the Wold-type decomposition of a pair of commuting isometries, Ann. Polon. Math. 37 (1980), 255-262. Zbl0485.47018

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