Properties of two variables Toeplitz type operators

Elżbieta Król-Klimkowska, Marek Ptak

Abstract


The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded.
We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.

Keywords


pair of contractions; isometric dilation; doubly commuting; Toeplitz operator; symbol operator

Mathematics Subject Classification (2010)


Primary 47B35; secondary 47B38.

References


Douglas, Ronald G. "On the operator equation $S* XT=X$ and related topics." Acta Sci. Math. (Szeged) 30 (1969): 19-32.

Halmos, Paul R. Introduction to Hilbert Space and the theory of Spectral Multiplicity. New York, N. Y.: Chelsea Publishing Company, 1951.

Jewell, Nicholas P., and Arthur R. Lubin."Commuting weighted shifts and analytic function theory in several variables." J. Operator Theory 1, no. 2 (1979): 207-223.

Kosiek, Marek. Functional calculus and common invariant subspaces. Kraków: Wydawnictwo Uniwersytetu Jagiellońskiego, 2001.

Kosiek, Marek, and Marek Ptak. "Reflexivity of N-tuples of contractions with rich joint left essential spectrum." Integral Equations Operator Theory 13, no. 3 (1990): 395-420.

Mancera, Carmen H., and Pedro J. Paúl. "Remarks, examples and spectral properties of generalized Toeplitz operators." Acta Sci. Math. (Szeged) 66, no. 3-4 (2000): 737-753.

Mlak, Włodzimierz. Wstęp do teorii przestrzeni Hilberta. Warszawa: PWN, 1970.

Szőkefalvi-Nagy, Béla, and Ciprian Foiaş. Harmonic analysis of operators on Hilbert space. Amsterdam-London: North-Holland Publishing Co., 1970.

Ptak, Marek. "On the reflexivity of multigenerator algebras." Dissertationes Math. 378 (1998): 1-61.

Ptak, Marek. "Two variables Toeplitz type operators." Acta Sci. Math. (Szeged) 71, no. 1-2 (2005): 353-362.

Pták, Vlastimil, and Pavla Vrbová. "Operators of Toeplitz and Hankel type." Acta Sci. Math. (Szeged) 52, no. 1-2 (1988): 117-140.

Słociński, Marek. "Isometric dilation of doubly commuting contractions and related models." Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25, no. 12 (1977): 1233-1242.

Słociński, Marek. "On the Wold-type decomposition of a pair of commuting isometries." Ann. Polon. Math. 37, no. 3 (1980): 255-262.


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