Operators on spaces of analytic functions
Seddighi, K.
Studia Mathematica, Tome 108 (1994), p. 49-54 / Harvested from The Polish Digital Mathematics Library
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Let Mz be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that Mz is polynomially bounded if ∥Mp∥≤C∥p∥G for every polynomial p. We give necessary and sufficient conditions for Mz 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.

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:216039 
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Seddighi, K. Operators on spaces of analytic functions. Studia Mathematica, Tome 108 (1994) pp. 49-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv108i1p49bwm/

[00000] [1] G. Adams, P. McGuire and V. Paulsen, Analytic reproducing kernels and multiplication operators, Illinois J. Math. 36 (1992), 404-419. | Zbl 0760.47010

[00001] [2] H. Hedenmalm and A. Shields, Invariant subspaces in Banach spaces of analytic functions, Michigan Math. J. 37 (1990), 91-104. | Zbl 0701.46044

[00002] [3] S. Richter, Invariant subspaces in Banach spaces of analytic functions, Trans. Amer. Math. Soc. 304 (1987), 585-616. | Zbl 0646.47023

[00003] [4] D. Sarason, Weak-star generators of H∞, Pacific J. Math. 17 (1966), 519-528. | Zbl 0171.33704

[00004] [5] K. Seddighi and B. Yousefi, On the reflexivity of operators on function spaces, Proc. Amer. Math. Soc. 116 (1992), 45-52. | Zbl 0806.47026

[00005] [6] H. Shapiro, Reproducing kernels and Beurling's theorem, Trans. Amer. Math. Soc. 110 (1964), 448-458. | Zbl 0147.11403

[00006] [7] A. Shields and L. Wallen, The commutants of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971), 777-788. | Zbl 0207.13801

[00007] [8] A. M. Sinclair, Automatic Continuity of Linear Operators, London Math. Soc. Lecture Note Ser. 21, Cambridge Univ. Press, 1976. | Zbl 0313.47029