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1991 | 100 | 1 | 81-86

Tytuł artykułu

A model for some analytic Toeplitz operators

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Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
We present a change of variable method and use it to prove the equivalence to bundle shifts for certain analytic Toeplitz operators on the Banach spaces $H^p(G) (1 ≤ p < ∞)$. In Section 2 we see this approach applied in the analysis of essential spectra. Some partial results were obtained in [9] in the Hilbert space case.

Twórcy

autor
  • Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30, 31-027 Kraków, Poland

Bibliografia

  • [1] M. B. Abrahamse and R. G. Douglas, A class of subnormal operators related to multiply connected domains, Adv. in Math. 19 (1976), 106-148.
  • [2] M. B. Abrahamse and T. Kriete, The spectral multiplicity of a multiplication operator, Indiana Univ. Math. J. 22 (1973), 845-857.
  • [3] J. B. Conway, Spectral properties of certain operators on Hardy spaces of domains, Integral Equations Operator Theory 10 (1987), 659-706.
  • [4] C. C. Cowen, On equivalence of Teoplitz operators, J. Operator Theory 7 (1982), 167-172.
  • [5] H. Helson, Lectures on Invariant Subspaces, Academic Press, 1964.
  • [6] R. F. Olin, Functional relationships between a subnormal operator and its minimal normal extension, Pacific J. Math. 63 (1976), 221-229.
  • [7] K. Rudol, Spectral mapping theorems for analytic functional calculi, in: Operator Theory: Adv. Appl. 17, Birkhäuser, 1986, 331-340.
  • [8] K. Rudol, The generalised Wold Decomposition for subnormal operators, Integral Equations Operator Theory 11 (1988), 420-436.
  • [9] K. Rudol, On the bundle shifts and cluster sets, ibid. 12 (1989), 444-448.
  • [10] J. Spraker, The minimal normal extensions for $M_z$ on the Hardy space of a planar region, Trans. Amer. Math. Soc. 318 (1990), 57-67.
  • [11] D. V. Yakubovich, Riemann surface models of Toeplitz operators, in: Operator Theory: Adv. Appl. 42, Birkhäuser, 1989, 305-415.

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