The algebra generated by a pair of operator weighted shifts

• Autorzy: Marek Ptak
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

pairs of operator weighted shifts; reflexive algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1995
• Tom: 62
• Numer: 2
• Strony: 97-110

Daty

wydano

1995

otrzymano

1992-04-13

Twórcy

autor

Marek Ptak

• Institute of Mathematics, University of Agriculture, Królewska 6, 30-045 Kraków, Poland

Bibliografia

• [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.
• [2] A. Lambert, The algebra generated by an invertibly weighted shift, J. London Math. Soc. (2) 5 (1972), 741-747.
• [3] A. Lambert, Unitary equivalence and reducibility of invertibly weighted shifts, Bull. Austral. Math. Soc. 5 (1971), 157-173.
• [4] M. Ptak, Reflexivity of pairs of shifts, Proc. Amer. Math. Soc. 109 (1990), 409-415.
• [5] A. L. Shields and L. J. Wallen, The commutant of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971), 777-788.
• [6] M. Słociński, On the Wold-type decomposition of a pair of commuting isometries, Ann. Polon. Math. 37 (1980), 255-262.