Normal and quasinormal composition operators
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- by Robert Whitley PDF
- Proc. Amer. Math. Soc. 70 (1978), 114-118 Request permission
Abstract:
A bounded linear operator ${C_T}$ on ${L^2}(X,\Sigma ,m)$ is a composition operator if it is induced by a point mapping $T:X \to X$ via ${C_T}f = f \circ T$. Normal and quasinormal composition operators on a finite measure space are characterized: ${C_T}$ is normal iff T is measure preserving and ${T^{ - 1}}(\Sigma )$ is (essentially) all of $\Sigma ;{C_T}$ is quasinormal iff T is measure preserving.References
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N. Dunford and J. T. Schwartz, Linear operators. I, Interscience, New York, 1958.
- Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
- Eric A. Nordgren, Composition operators, Canadian J. Math. 20 (1968), 442–449. MR 223914, DOI 10.4153/CJM-1968-040-4
- William C. Ridge, Spectrum of a composition operator, Proc. Amer. Math. Soc. 37 (1973), 121–127. MR 306457, DOI 10.1090/S0002-9939-1973-0306457-2
- H. L. Royden, Real analysis, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1963. MR 0151555
- Raj Kishor Singh, Compact and quasinormal composition operators, Proc. Amer. Math. Soc. 45 (1974), 80–82. MR 348545, DOI 10.1090/S0002-9939-1974-0348545-1
- Raj Kishor Singh, Normal and Hermitian composition operators, Proc. Amer. Math. Soc. 47 (1975), 348–350. MR 355679, DOI 10.1090/S0002-9939-1975-0355679-5
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 70 (1978), 114-118
- MSC: Primary 47B38; Secondary 47B15
- DOI: https://doi.org/10.1090/S0002-9939-1978-0492057-5
- MathSciNet review: 492057