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Operators and Dynamical Systems on Weighted Function Spaces
Author(s) -
Singh R. K.,
Manhas J. S.
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941690120
Subject(s) - mathematics , hausdorff space , uniform norm , scalar multiplication , infimum and supremum , locally convex topological vector space , continuous functions on a compact hausdorff space , regular polygon , multiplication (music) , function space , norm (philosophy) , pure mathematics , vector space , discrete mathematics , combinatorics , topological space , geometry , elliptic curve , political science , law
Let X be a completely regular Hausdorff space, let V be a system of weights on X and let E be a locally convex Hausdorff space. Let CV 0 ( X, E ) and CV b ( X, E ) be the weighted locally convex spaces of vector‐valued continuous functions with a topology generated by seminorms which are weighted analogue of the supremum norm. In the present paper, we characterize multiplication operators and weighted composition operators on the spaces CV 0 ( X, E ) and CV b ( X, E ) induced by scalar‐valued and vector‐valued mappings. A (linear) dynamical system on these weighted spaces is obtained as an application of the theory of multiplication operators.