Commutative algebras of Toeplitz operators on the strip (in Russian) |
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Author |
ivanpribegin@rambler.ru
Odessa I.I. Mechnikov National University, Institute of Mathematics, Economics and Mechanics
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Abstract |
We show that $C^*$-algebras generated by Toeplitz operators on the Bergman space on the
strip with bounded measurable deffning symbols, depending only on real variable, are commutative.
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Keywords |
Bergman projection; Bergman space; Toeplitz operator
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DOI |
doi:10.15330/ms.45.1.98-103
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Reference |
1. Dzhuraev A.D. Methods of singulare integral equations. - M.: Press Nauka, 1987, 416 p. (in Russian)
2. Vasilevski N.L. Commutative algebras of Toeplitz operators on the Bergman space// Series Operator Theory: Advances Applications. - 2008, V.XXIX, 1985, 417 p. 3. Korenblum B., Kehe Zhu An applicationn on Tauberian theorems to Toeplitz operators// J. Operator Theory. - 1995. - V.33. - P. 353-361. 4. Grudsky S., Karapetyants A., Vasilevski N. Toeplitz operators on the unit ball in $\mathbb{C}^n$ with radial symbols// J. Operator Theory. - 2003. - V.49. - P. 325-346. 5. Karapetyants A.N. The space $BMO_\lambda^p(\mathbb{D})$, compact Toeplitz operators with $BMO_\lambda^1(\mathbb{D})$ symbols on weighted Bergman spaces, and Berezin transform// Izv. Vyssh. Uchebn. Zaved. Mat. - 2006. - V.8(531). - P. 76-79. (in Russian) 6. Ze-Hua Zhou, Xing-Tang Dong Algebraic properties of Teoplitz operators with radial symbols on the unit ball// Iutegr. equ. oper. theory. - 2009. - V.64. - P. 137-154. 7. Zhi Ling Sun, Yu Feng Lu Toeplitz operators on the weighted pluriharmonic Bergman space with radial symbols// Abstract and Applied Analysis. - 2011. - Article ID 210596. - 15 p. 8. Mikhlin S.G., Prosdorf S. Singulare integral operators. - Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1986. 9. Simonenko I.B., Chin Ngok Min Lokal method in the theory of one-dimensional singular integral equations with picewise continuous coefficients. Noetherity. - University Press, Rostov-on-Don, 1983, 84 p. (in Russian) 10. Bateman H., Erdelyi A. Tables of integral transforms. - V.1, Fourier, Laplas and Mellin transforms, M.:Press Nauka, 1969, 343 p. (in Russian) 11. Gelfand I.M., Raikow D.A., Shilov G.E. Commutative normed rings. - M.: Press Fiz. Mat. Lit., 1960, 316 p. (in Russian) |
Pages |
98-103
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Volume |
45
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Issue |
1
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Year |
2016
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Journal |
Matematychni Studii
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Full text of paper | |
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