Abstract
In this note we characterize the compact and weakly compact weighted composition operatorsW π,ϕ on certain weighted locally convex spacesCV o(X, E) of vector-valued continuous functions induced by self maps ϕ ofX and the operator-valued mappings π ∶X→B(E).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K.-D. Bierstedt. Gewichtete Räume Vektor Wertiger Functionen und das Injective Tensor Product I,II,J. Reine Angew. Math., 259, 186–210, 260, 133–146, 1973.
J. T. Chan. Operators with the disjoint support property.J. Operator Theory, 24, 383–391, 1990.
W. Feldman. Compact weighted composition operators on Banach lattices.Proc. Amer. Math. Soc., 108, 95–99, 1990.
J. E. Jamison and M. Rajagopalan. Weighted composition operators onC(X, E).J. Operator Theory, 19, 307–317, 1988.
H. Kamowitz. Compact weighted endomorphisms ofC(X).Proc. Amer. Math. Soc., 83, 517–521, 1981.
M. Lindström and J. Llavona. Compact and weakly compact homomorphisms between algebras of continuous functions.J. Math. Anal. Appl., 166, 325–330, 1992.
L. Nachbin.Elements of Approximation Theory, Math. Studies 14, Van Nostrand, Princeton, 1967.
J. B. Prolla. Weighted spaces of vector-valued continuous functions.Ann. Mat. Pura Appl., 89, 145–158, 1971.
W. M. Ruess and W. H. Summers. Compactness in spaces of vector-valued continuous functions and asymptotic almost periodicity.Math. Nachr., 135, 7–33, 1988.
W. M. Ruess and W. H. Summers. Integration of asymptotically almost periodic functions with weak asymptotic almost periodicity.Dissertationes Math., 279, 1989.
R. K. Singh and J. S. Manhas,Composition Operators on Function Spaces. North Holland Math. Studies, 179, Elsevier Science Publishers, Amsterdam, New York, 1993.
R. K. Singh, J. S. Manhas and B. Singh. Compact operators of composition on some locally convex function spaces.J. Operator Theory, 31, 11–20, 1994.
R. K. Singh and W. H. Summers. Compact and weakly compact composition operators on spaces of vector-valued continuous functions.Proc. Amer. Math. Soc., 99, 667–670, 1987.
H. Takagi. Compact weighted composition operators on certain subspaces ofC(X, E).Tokyo J. Math., 14, 121–127, 1991.
Author information
Authors and Affiliations
Additional information
The work of this author was supported in part by CSIR Grant 9/100/92-EMR-I
The work of this author was supported in part by UGC Grant F.8-7/91 (RBB-II)
Rights and permissions
About this article
Cite this article
Manhas, J.S., Singh, R.K. Compact and weakly compact weighted composition operators on weighted spaces of continuous functions. Integr equ oper theory 29, 63–69 (1997). https://doi.org/10.1007/BF01191480
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01191480