×

Fredholm multiplication and composition operators on the Hardy space. (English) Zbl 0723.47024

Summary: We present a unified approach to the problem of characterizing the Fredholm multiplication and composition operators on the Hardy space \(H^ 2\).

MSC:

47B38 Linear operators on function spaces (general)
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
47A53 (Semi-) Fredholm operators; index theories
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] S. Axler and P. Bourdon,Finite Codimensional Invariant Subspaces of Bergman Spaces, Trans. Amer. Math. Soc. 306 (1988), 805-817. · Zbl 0658.47011
[2] J. A. Cima, J. E. Thomson, And W. R. Wogen,On some properties of composition operators, Indiana Univ. Math. J. 24 (1974), 215-220. · Zbl 0284.47026 · doi:10.1512/iumj.1974.24.24018
[3] P. Duren,Theory of H p spaces, Academic Press, New York, 1970. · Zbl 0215.20203
[4] R. Gellar,Cyclic vectors and parts of the spectrum of a weighted shift, Trans. Amer. Math. Soc. 146 (1969), 69-85. · Zbl 0207.13201 · doi:10.1090/S0002-9947-1969-0259642-6
[5] D. Sarason,Invariant subspaces and unstarred operator algebras, Pacific J. Math. 17 (1966), 511-517. · Zbl 0171.33703
[6] H. J. Schwartz,Composition operators on H p , Thesis, University of Toledo, 1969.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.