# The algebra generated by a pair of operator weighted shifts

Annales Polonici Mathematici (1995)

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

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topMarek 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

top- [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] A. Lambert, The algebra generated by an invertibly weighted shift, J. London Math. Soc. (2) 5 (1972), 741-747. Zbl0244.46079
- [3] A. Lambert, Unitary equivalence and reducibility of invertibly weighted shifts, Bull. Austral. Math. Soc. 5 (1971), 157-173. Zbl0217.45303
- [4] M. Ptak, Reflexivity of pairs of shifts, Proc. Amer. Math. Soc. 109 (1990), 409-415. Zbl0734.47023
- [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] 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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