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2015 | OriginalPaper | Buchkapitel

7. Similarity and Unitary Equivalence

verfasst von : Kunyu Guo, Hansong Huang

Erschienen in: Multiplication Operators on the Bergman Space

Verlag: Springer Berlin Heidelberg

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Abstract

In this chapter, we will apply those methods developed in Chaps. 3–6 to study similarity and unitary equivalence of multiplication operators, defined on both the Hardy space and the Bergman space.

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Literatur
[CG]
Zurück zum Zitat X. Chen, K. Guo, Analytic Hilbert Modules. π-Chapman & Hall/CRC Research Notes in Mathematics, vol. 433, (2003) X. Chen, K. Guo, Analytic Hilbert Modules. π-Chapman & Hall/CRC Research Notes in Mathematics, vol. 433, (2003)
[Cla1]
Zurück zum Zitat D. Clark, On Toeplitz operators with loops. J. Oper. Theory 4, 37–54 (1980)MATH D. Clark, On Toeplitz operators with loops. J. Oper. Theory 4, 37–54 (1980)MATH
[Cla2]
Zurück zum Zitat D. Clark, On a similarity theory for rational Toeplitz operators. J. Riene Angew. Math. 320, 6–31 (1980)MATH D. Clark, On a similarity theory for rational Toeplitz operators. J. Riene Angew. Math. 320, 6–31 (1980)MATH
[Cla3]
Zurück zum Zitat D. Clark, On Toeplitz operators with loops II. J. Oper. Theory 7, 109–123 (1982)MATH D. Clark, On Toeplitz operators with loops II. J. Oper. Theory 7, 109–123 (1982)MATH
[Cla4]
Zurück zum Zitat D. Clark, Sz-Nagy-Foias theory and similarity for a class of Toeplitz operators, in Proceedings of the 1977 Spectral theory Semester (The Stefan Banach Mathematical Center, Warsaw, 1982) D. Clark, Sz-Nagy-Foias theory and similarity for a class of Toeplitz operators, in Proceedings of the 1977 Spectral theory Semester (The Stefan Banach Mathematical Center, Warsaw, 1982)
[Cow3]
Zurück zum Zitat C. Cowen, An analytic Toeplitz operator that commutes with a compact operator and a related class of Toeplitz operators. Funct. Anal. 36, 169–184 (1980)MATHMathSciNetCrossRef C. Cowen, An analytic Toeplitz operator that commutes with a compact operator and a related class of Toeplitz operators. Funct. Anal. 36, 169–184 (1980)MATHMathSciNetCrossRef
[Cow4]
[CW]
Zurück zum Zitat C. Cowen, R. Wahl, Commutants of finite Blaschke product multiplication operators. Preprint C. Cowen, R. Wahl, Commutants of finite Blaschke product multiplication operators. Preprint
[Dou]
Zurück zum Zitat R. Douglas, Operator theory and complex geometry. Extracta Math. 24, 135–165 (2009). arXiv: math.FA/ 0710.1880v2 R. Douglas, Operator theory and complex geometry. Extracta Math. 24, 135–165 (2009). arXiv: math.FA/ 0710.1880v2
[DPa]
Zurück zum Zitat R. Douglas, V. Paulsen, Hilbert Modules over Function Algebras. Pitman Research Notes in Mathematics, vol. 217 (Longman Scientific & Technical, Harlow, 1989) R. Douglas, V. Paulsen, Hilbert Modules over Function Algebras. Pitman Research Notes in Mathematics, vol. 217 (Longman Scientific & Technical, Harlow, 1989)
[DS]
Zurück zum Zitat P. Duren, A. Schuster, Bergman Spaces. Mathematics Surveys and Monographs, vol. 100 (American Mathematical Society, Rhode Island, 2004) P. Duren, A. Schuster, Bergman Spaces. Mathematics Surveys and Monographs, vol. 100 (American Mathematical Society, Rhode Island, 2004)
[Dur]
[Ga]
Zurück zum Zitat J. Garnett, Bounded Analytic Functions (Academic, New York, 1981)MATH J. Garnett, Bounded Analytic Functions (Academic, New York, 1981)MATH
[GH1]
Zurück zum Zitat K. Guo, H. Huang, On multiplication operators of the Bergman space: similarity, unitary equivalence and reducing subspaces. J. Oper. Theory 65, 355–378 (2011)MATHMathSciNet K. Guo, H. Huang, On multiplication operators of the Bergman space: similarity, unitary equivalence and reducing subspaces. J. Oper. Theory 65, 355–378 (2011)MATHMathSciNet
[Guo1]
Zurück zum Zitat K. Guo, Algebraic reduction for Hardy submodules over polydisk algebras. J. Oper. Theory 41, 127–138 (1999)MATH K. Guo, Algebraic reduction for Hardy submodules over polydisk algebras. J. Oper. Theory 41, 127–138 (1999)MATH
[Guo2]
[Guo4]
[Guo5]
Zurück zum Zitat K. Guo, Operator theory and Von Neumann algebras (a manuscript) K. Guo, Operator theory and Von Neumann algebras (a manuscript)
[Guo6]
Zurück zum Zitat K. Guo, Defect operators for submodules of H d 2. J. Reine Angew. Math. 573, 181–209 (2004) K. Guo, Defect operators for submodules of H d 2. J. Reine Angew. Math. 573, 181–209 (2004)
[GW1]
Zurück zum Zitat K. Guo, K. Wang, On operators which commute with analytic Toeplitz operators modulo the finite rank operators. Proc. Am. Math. Soc. 134, 2571–2576 (2006)MATHCrossRef K. Guo, K. Wang, On operators which commute with analytic Toeplitz operators modulo the finite rank operators. Proc. Am. Math. Soc. 134, 2571–2576 (2006)MATHCrossRef
[GW2]
Zurück zum Zitat K. Guo, K. Wang, Essentially normal Hilbert modules and K-homology II: quasi-homogeneous Hilbert modules over the two dimensional unit ball. J. Ramanujan Math. Soc. 22, 259–281 (2007)MATHMathSciNet K. Guo, K. Wang, Essentially normal Hilbert modules and K-homology II: quasi-homogeneous Hilbert modules over the two dimensional unit ball. J. Ramanujan Math. Soc. 22, 259–281 (2007)MATHMathSciNet
[GW4]
Zurück zum Zitat K. Guo, K. Wang, Beurling type quotient modules over the bidisk and boundary representations. J. Funct. Anal. 257, 3218–3238 (2009)MATHMathSciNetCrossRef K. Guo, K. Wang, Beurling type quotient modules over the bidisk and boundary representations. J. Funct. Anal. 257, 3218–3238 (2009)MATHMathSciNetCrossRef
[Hof1]
Zurück zum Zitat K. Hoffman, Banach Spaces of Analytic Functions (Prentice-Hall, Englewood Cliffs, 1962)MATH K. Hoffman, Banach Spaces of Analytic Functions (Prentice-Hall, Englewood Cliffs, 1962)MATH
[JL]
Zurück zum Zitat C. Jiang, Y. Li, The commutant and similarity invariant of analytic Toeplitz operators on Bergman space. Sci. China Ser. A 5, 651–664 (2007)CrossRef C. Jiang, Y. Li, The commutant and similarity invariant of analytic Toeplitz operators on Bergman space. Sci. China Ser. A 5, 651–664 (2007)CrossRef
[JZ]
[Pel]
Zurück zum Zitat V. Peller, Hankel Operators and Their Applications. Springer Monographs in Mathematics (Springer, New York, 2003) V. Peller, Hankel Operators and Their Applications. Springer Monographs in Mathematics (Springer, New York, 2003)
[Ru1]
Zurück zum Zitat W. Rudin, Function Theory in Polydiscs (Benjamin, New York, 1969)MATH W. Rudin, Function Theory in Polydiscs (Benjamin, New York, 1969)MATH
[Shi]
Zurück zum Zitat A. Shields, Weighted Shift Operators and Analytic Function Theory. Mathematical Surveys, vol. 13 (American mathematical Society, Providence, 1974), 49–128 A. Shields, Weighted Shift Operators and Analytic Function Theory. Mathematical Surveys, vol. 13 (American mathematical Society, Providence, 1974), 49–128
[Sun1]
Zurück zum Zitat S. Sun, On unitary equivalence of multiplication operators on Bergman space. Northeast. Math. J. 1, 213–222 (1985)MATHMathSciNet S. Sun, On unitary equivalence of multiplication operators on Bergman space. Northeast. Math. J. 1, 213–222 (1985)MATHMathSciNet
[SY]
Zurück zum Zitat S. Sun, D. Yu, On unitary equivalence of multiplication operators on Bergman space (II). Northeast. Math. J. 4, 169–179 (1988)MATHMathSciNet S. Sun, D. Yu, On unitary equivalence of multiplication operators on Bergman space (II). Northeast. Math. J. 4, 169–179 (1988)MATHMathSciNet
[SZZ1]
Zurück zum Zitat S. Sun, D. Zheng, C. Zhong, Classification of reducing subspaces of a class of multiplication operators via the Hardy space of the bidisk. Can. J. Math. 62, 415–438 (2010)MATHMathSciNetCrossRef S. Sun, D. Zheng, C. Zhong, Classification of reducing subspaces of a class of multiplication operators via the Hardy space of the bidisk. Can. J. Math. 62, 415–438 (2010)MATHMathSciNetCrossRef
[SZZ2]
Zurück zum Zitat S. Sun, D. Zheng, C. Zhong, Multiplication operators on the Bergman space and weighted shifts. J. Oper. Theory 59, 435–452 (2008)MATHMathSciNet S. Sun, D. Zheng, C. Zhong, Multiplication operators on the Bergman space and weighted shifts. J. Oper. Theory 59, 435–452 (2008)MATHMathSciNet
Metadaten
Titel
Similarity and Unitary Equivalence
verfasst von
Kunyu Guo
Hansong Huang
Copyright-Jahr
2015
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-46845-6_7