Lamperti-type operators on a weighted space of continuous functions
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- by R. K. Singh and Bhopinder Singh PDF
- Proc. Amer. Math. Soc. 125 (1997), 1161-1165 Request permission
Abstract:
For a locally convex Hausdorff topological vector space $E$ and for a system $V$ of weights vanishing at infinity on a locally compact Hausdorff space $X$, let $CV_0(X,E)$ be the weighted space of $E$-valued continuous functions on $X$ with the locally convex topology derived from the seminorms which are weighted analogues of the supremum norm. A characterization of the orthogonality preserving (Lamperti-type) operators on $CV_0(X,E)$ is presented in this paper.References
- Yuri A. Abramovich, Multiplicative representation of disjointness preserving operators, Nederl. Akad. Wetensch. Indag. Math. 45 (1983), no. 3, 265–279. MR 718068, DOI 10.1016/1385-7258(83)90062-8
- Y. A. Abramovich, E. L. Arenson, and A. K. Kitover, Banach $C(K)$-modules and operators preserving disjointness, Pitman Research Notes in Mathematics Series, vol. 277, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1992. MR 1202880
- Wolfgang Arendt, Spectral properties of Lamperti operators, Indiana Univ. Math. J. 32 (1983), no. 2, 199–215. MR 690185, DOI 10.1512/iumj.1983.32.32018
- Jor-Ting Chan, Operators with the disjoint support property, J. Operator Theory 24 (1990), no. 2, 383–391. MR 1150627
- James E. Jamison and M. Rajagopalan, Weighted composition operator on $C(X,E)$, J. Operator Theory 19 (1988), no. 2, 307–317. MR 960982
- João B. Prolla, Weighted approximation of continuous functions, Bull. Amer. Math. Soc. 77 (1971), 1021–1024. MR 290014, DOI 10.1090/S0002-9904-1971-12845-8
- R. K. Singh and J. S. Manhas, Composition operators on function spaces, North-Holland Mathematics Studies, vol. 179, North-Holland Publishing Co., Amsterdam, 1993. MR 1246562, DOI 10.1016/S0304-0208(08)71589-5
- R. K. Singh and Bhopinder Singh, Weighted composition operators on a space of vector-valued functions, Far East J. Math. Sci. 2 (1994), 95–100.
- W. H. Summers, Weighted locally convex spaces of continuous functions, Ph. D. Thesis, Louisiana State University, 1968.
Additional Information
- R. K. Singh
- Affiliation: Department of Mathematics, University of Jammu, Jammu 180 004, India
- Bhopinder Singh
- Affiliation: Department of Mathematics, University of Jammu, Jammu 180 004, India
- Address at time of publication: Department of Mathematics, Government College of Engineering and Technology, Jammu 180 001, India
- Received by editor(s): April 14, 1995
- Received by editor(s) in revised form: October 23, 1995
- Additional Notes: The second author was supported by NBHM(DAE) Grant No. 40/16/93-G
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1161-1165
- MSC (1991): Primary 47B38, 46E40, 47B60
- DOI: https://doi.org/10.1090/S0002-9939-97-03717-9
- MathSciNet review: 1363437