A model for some analytic Toeplitz operators

• Autorzy: K. Rudol
• 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.

Kategorie tematyczne

• 46J15: Banach algebras of differentiable or analytic functions, H p -spaces
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1991
• Tom: 100
• Numer: 1
• Strony: 81-86

Daty

wydano

1991

otrzymano

1990-12-12

Twórcy

autor

K. Rudol

• 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.