On Some Bergman Shift Operators

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• 作者：Olof Giselsson (1) olofg@maths.lth.se
  Anders Olofsson (1) olofsson@maths.lth.se
• 关键词：Bergman shift operator – ; Wold decomposition – ; Invariant subspace – ; n ; Isometry
• 刊名：Complex Analysis and Operator Theory
• 出版年：2012
• 出版时间：August 2012
• 年：2012
• 卷：6
• 期：4
• 页码：829-842
• 全文大小：232.2 KB
• 参考文献：1. Agler J.: The Arveson extension theorem and coanalytic models. Integral Equ. Oper. Theory 5, 608–631 (1982)
  2. Agler J.: Hypercontractions and subnormality. J. Oper. Theory 13, 203–217 (1985)
  3. Agler J., Stankus M.: m-Isometric transformations of Hilbert space I. Integral Equ. Oper. Theory 21, 383–429 (1995)
  4. Agler J., Stankus M.: m-Isometric transformations of Hilbert space II. Integral Equ. Oper. Theory 23, 1–48 (1995)
  5. Agler J., Stankus M.: m-Isometric transformations of Hilbert space III. Integral Equ. Oper. Theory 24, 379–421 (1996)
  6. Aleman, A.: The multiplication operator on Hilbert spaces of analytic functions, Habilitationsschrift, FernUniversit盲t Hagen (1993)
  7. Aleman A., Richter S., Sundberg C.: Beurling’s theorem for the Bergman space. Acta Math. 177, 275–310 (1996)
  8. Chalendar I., Partington J.R.: Doubly-invariant subspaces for the shift on the vector-valued Sobolev spaces of the disc and annulus. Integral Equ. Oper. Theory 61, 149–158 (2008)
  9. Gelfand I., Raikov D., Shilov G.: Commutative Normed Rings. Chelsea Publishing Co., New York (1964)
  10. Halmos P.R.: Shifts on Hilbert spaces. J. Reine Angew. Math. 208, 102–112 (1961)
  11. Hanin L.G.: Spectral synthesis of ideals in algebras of functions having generalized derivatives. Usp. Math. Nauk 39, 199–200 (1984)
  12. Hedenmalm H., Jakobsson S., Shimorin S.: A biharmonic maximum principle for hyperbolic surfaces. J. Reine Angew. Math. 550, 25–75 (2002)
  13. Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman spaces. In: Graduate Texts in Mathematics, vol. 199, Springer, New York (2000)
  14. Louhichi I., Olofsson A.: Characterizations of Bergman space Toeplitz operators with harmonic symbols. J. Reine Angew. Math. 617, 1–26 (2008)
  15. Olofsson A.: A von Neumann Wold decomposition of two-isometries. Acta Sci. Math. (Szeged) 70, 715–726 (2004)
  16. Olofsson A.: Wandering subspace theorems. Integral Equ. Oper. Theory 51, 395–409 (2005)
  17. Olofsson A.: A characteristic operator function for the class of n-hypercontractions. J. Funct. Anal. 236, 517–545 (2006)
  18. Olofsson A.: An operator-valued Berezin transform and the class of n-hypercontractions. Integral Equ. Oper. Theory 58, 503–549 (2007)
  19. Richter S.: Invariant subspaces of the Dirichlet shift. J. Reine Angew. Math. 386, 205–220 (1988)
  20. Shimorin S.: Wold-type decompositions and wandering subspaces for operators close to isometries. J. Reine Angew. Math. 531, 147–189 (2001)
  21. Sz.-Nagy, B., Foias, C.: Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam (1970)
• 作者单位：1. Department of Mathematics, Faculty of Science, Centre for Mathematical Sciences, Lund University, P.O. Box 118, 221 00 Lund, Sweden
• ISSN：1661-8262

文摘

An operator identity satisfied by the shift operator in a class of standard weighted Bergman spaces is studied. We show that subject to a pureness condition this operator identity characterizes the associated Bergman shift operator up to unitary equivalence allowing for a general multiplicity. The analysis of the general case makes contact with the class of n-isometries studied by Agler and Stankus.