Operators on spaces of analytic functions

• Autorzy: K. Seddighi
• Języki publikacji: EN

Abstrakty

EN

Let $M_z$ be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that $M_z$ is polynomially bounded if $∥M_p∥ ≤ C∥p∥_G$ for every polynomial p. We give necessary and sufficient conditions for $M_z$ to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.

Słowa kluczowe

EN

spaces of analytic functions; polynomially bounded; multipliers; spectral properties; cyclic subspace

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 47A25: Spectral sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 108
• Numer: 1
• Strony: 49-54

Daty

wydano

1994

otrzymano

1992-10-13

poprawiono

1993-07-05

Twórcy

autor

K. Seddighi

• Department of Mathematics & Statistics, College of Sciences, Shiraz University, Shiraz 71454, Islamic Republic of Iran

Bibliografia

• [1] G. Adams, P. McGuire and V. Paulsen, Analytic reproducing kernels and multiplication operators, Illinois J. Math. 36 (1992), 404-419.
• [2] H. Hedenmalm and A. Shields, Invariant subspaces in Banach spaces of analytic functions, Michigan Math. J. 37 (1990), 91-104.
• [3] S. Richter, Invariant subspaces in Banach spaces of analytic functions, Trans. Amer. Math. Soc. 304 (1987), 585-616.
• [4] D. Sarason, Weak-star generators of $H^∞$, Pacific J. Math. 17 (1966), 519-528.
• [5] K. Seddighi and B. Yousefi, On the reflexivity of operators on function spaces, Proc. Amer. Math. Soc. 116 (1992), 45-52.
• [6] H. Shapiro, Reproducing kernels and Beurling's theorem, Trans. Amer. Math. Soc. 110 (1964), 448-458.
• [7] A. Shields and L. Wallen, The commutants of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971), 777-788.
• [8] A. M. Sinclair, Automatic Continuity of Linear Operators, London Math. Soc. Lecture Note Ser. 21, Cambridge Univ. Press, 1976.