Properties of two variables Toeplitz type operators

Elżbieta Król-Klimkowska; Marek Ptak

doi:10.1515/aupcsm-2016-0008

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Properties of two variables Toeplitz type operators

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 15 (2016): Issue 1 (December 2016)

By: Elżbieta Król-Klimkowska and Marek Ptak

Open Access

|Dec 2016

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.

References

[1] Douglas, Ronald G. “On the operator equation S*XT = X and related topics.” Acta Sci. Math. (Szeged) 30 (1969): 19–32. Cited on 97 and 102.
Search in Google Scholar Back to article
[2] Halmos, Paul R. Introduction to Hilbert Space and the theory of Spectral Multiplicity. New York, N. Y.: Chelsea Publishing Company, 1951. Cited on 102.
Search in Google Scholar Back to article
[3] 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. Cited on 104.
Search in Google Scholar Back to article
[4] Kosiek, Marek. Functional calculus and common invariant subspaces. Kraków: Wydawnictwo Uniwersytetu Jagiellońskiego, 2001. Cited on 102.
Search in Google Scholar Back to article
[5] 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. Cited on 102.
Search in Google Scholar Back to article
[6] 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. Cited on 97.
Search in Google Scholar Back to article
[7] Mlak, Włodzimierz. Wstęp do teorii przestrzeni Hilberta. Warszawa: PWN, 1970. Cited on 104.
Search in Google Scholar Back to article
[8] Szőkefalvi-Nagy, Béla, and Ciprian Foiaş. Harmonic analysis of operators on Hilbert space. Amsterdam-London: North-Holland Publishing Co., 1970. Cited on 98.
Search in Google Scholar Back to article
[9] Ptak, Marek. “On the reflexivity of multigenerator algebras.” Dissertationes Math. 378 (1998): 1–61. Cited on 98.
Search in Google Scholar Back to article
[10] Ptak, Marek. “Two variables Toeplitz type operators.” Acta Sci. Math. (Szeged) 71, no. 1-2 (2005): 353–362. Cited on 98, 99, 100, 101 and 104.
Search in Google Scholar Back to article
[11] Pták, Vlastimil, and Pavla Vrbová. “Operators of Toeplitz and Hankel type.” Acta Sci. Math. (Szeged) 52, no. 1-2 (1988): 117–140. Cited on 97.
Search in Google Scholar Back to article
[12] 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. Cited on 98 and 99.
Search in Google Scholar Back to article
[13] Słociński, Marek. “On the Wold-type decomposition of a pair of commuting isometries.” Ann. Polon. Math. 37, no. 3 (1980): 255–262. Cited on 98.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/aupcsm-2016-0008 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 97 - 106

Submitted on: May 23, 2016

Accepted on: Oct 14, 2016

Published on: Dec 23, 2016

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Pair of contractions,

Related subjects:

© 2016 Elżbieta Król-Klimkowska, Marek Ptak, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 15 (2016): Issue 1 (December 2016)