OPERATORS ON BANACH ALGEBRA VALUED FUNCTION SPACES

Article Sidebar

PDF
Published: Sep 1, 1992
DOI: https://doi.org/10.5556/j.tkjm.23.1992.4546
Keywords:
Representing measures multiplicative operators multiplicatively symmetric operators Arens product

Main Article Content

JOR-TING CHAN
Department of Mathematics, University of Hong Kong, Hong Kong.

Abstract




Let $S$ be a locally compact Hausdorff space and let $A$ be a Banach algebra. Denote by $C_0(S, A)$ the Banach algebra of all $A$-valued continuous functions vanishing at infinity on $S$. Properties of bounded linear operators on $C_0(S,A)$, like multiplicativity, are characterized by Choy in terms of their representing measures. We study these theorems and give sharper results in certain cases.




Article Details

How to Cite
CHAN, J.-T. (1992). OPERATORS ON BANACH ALGEBRA VALUED FUNCTION SPACES. Tamkang Journal of Mathematics, 23(3), 233–238. https://doi.org/10.5556/j.tkjm.23.1992.4546
Issue
Vol. 23 No. 3 (1992)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

J. Batt and E. J. Berg, "Linear hounded transformations on the space of continuous functions," J. Funct. Anal. 4(1969), 215-239.

F. F. Bonsall and J. Duncan, "Numerical Ranges of Operators on Normed space and of Elements of Normed Algebras," London Math. Soc. Lecture Note Series, Vol. 2, Cambridge Univ. Press, London-New York, 1971.

S. T. L. Choy, "Integral representation oi multiplicative, involution preserving operators in L(Co(S,A), B)," Proc. Amer. Math. Soc. 83(1981), 54-58.

----, "One-to-one opera.tors on function spaces," ibid 87(1983),691-694.