Back to Search
Start Over
MULTIPLICATION OPERATORS ON VECTOR-VALUED FUNCTION SPACES.
- Source :
-
Proceedings of the American Mathematical Society . Oct2013, Vol. 141 Issue 10, p3501-3513. 13p. - Publication Year :
- 2013
-
Abstract
- Let E be a Banach function space on a probability measure space (Ω,Σ,μ). Let X be a Banach space and E(X) be the associated Kothe-Bochner space. An operator on E(X) is called a multiplication operator if it is given by multiplication by a function in L∞(μ). In the main result of this paper, we show that an operator T on E(X) is a multiplication operator if and only if T commutes with L∞(μ) and leaves invariant the cyclic subspaces generated by the constant vector-valued functions in E(X). As a corollary we show that this is equivalent to T satisfying a functional equation considered by Calabuig, Rodr'ıguez, and S'anchez-P'erez. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 141
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 89472723
- Full Text :
- https://doi.org/10.1090/S0002-9939-2013-11603-5