Compact weighted composition operators on $L^ p$
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- by Hiroyuki Takagi PDF
- Proc. Amer. Math. Soc. 116 (1992), 505-511 Request permission
Abstract:
We characterize the compact weighted composition operators on ${L^p}(1 \leq p < \infty )$ and determine their spectra. We also show that every weakly compact weighted composition operator on ${L^1}$ is compact.References
- James W. Carlson, The spectra and commutants of some weighted composition operators, Trans. Amer. Math. Soc. 317 (1990), no. 2, 631–654. MR 979958, DOI 10.1090/S0002-9947-1990-0979958-6
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
- William Feldman, Compact weighted composition operators on Banach lattices, Proc. Amer. Math. Soc. 108 (1990), no. 1, 95–99. MR 990422, DOI 10.1090/S0002-9939-1990-0990422-6
- Herbert Kamowitz, Compact weighted endomorphisms of $C(X)$, Proc. Amer. Math. Soc. 83 (1981), no. 3, 517–521. MR 627682, DOI 10.1090/S0002-9939-1981-0627682-1
- Eric A. Nordgren, Composition operators on Hilbert spaces, Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977) Lecture Notes in Math., vol. 693, Springer, Berlin, 1978, pp. 37–63. MR 526531
- 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
- 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
- R. K. Singh and Ashok Kumar, Compact composition operators, J. Austral. Math. Soc. Ser. A 28 (1979), no. 3, 309–314. MR 557280, DOI 10.1017/S1446788700012258
- R. K. Singh and R. David Chandra Kumar, Compact weighted composition operators on $L^2(\lambda )$, Acta Sci. Math. (Szeged) 49 (1985), no. 1-4, 339–344. MR 839949
- R. K. Singh and N. S. Dharmadhikari, Compact and Fredholm composite multiplication operators, Acta Sci. Math. (Szeged) 52 (1988), no. 3-4, 437–441. MR 980291
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 505-511
- MSC: Primary 47B38; Secondary 47B07
- DOI: https://doi.org/10.1090/S0002-9939-1992-1097354-8
- MathSciNet review: 1097354