Abstract
Characterizations of multipliers on algebras of continuous functions with values in a commutative Banach or \(C^{*}\)-algebra A have been obtained by several authors. In this paper, we investigate the extent to which these characterizations can be made beyond Banach algebras. We shall focus mainly on the algebras of continuous functions with values in an F-algebra A (not necessarily locally convex), in particular in a complete p-normed algebra, \(0<p\le 1,\) having a minimal approximate identity. We include a few examples related to our results. Most of our initial results remain valid without the commutativity of A.
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References
Abel, M.: Topological bimodule-algebras. In: Proceedings of the 3rd International Conference on Topological Algebras and Applications, Oulu, Finland, pp. 25–42, 2004
Adib, M., Riazi, A.H., Khan, L.A.: Quasi-multipliers on F- algebras. Abstr Appl Anal 2011, Article ID 235273 (2011)
Akemann, C.A., Pedersen, G.K., Tomiyama, J.: Multipliers of \(C^{\ast }\)-algebras. J. Funct. Anal. 13, 277–301 (1973)
Ansari-Piri, E.: A class of factorizable topological algebras. Proc. Edinb. Math. Soc. 33, 53–59 (1990)
Bonsall, F.F., Duncan, J.: Complete Normed Algebras. Springer, New York (1973)
Buck, R.C.: Bounded continuous functions on a locally compact space. Mich. Math. J. 5, 95–104 (1958)
Busby, R.C.: Double centralizers and extension of \(C^{\ast }\)-algebras. Trans. Am. Math. Soc. 132, 79–99 (1968)
Haro, J.C.C., Lai, H.C.: Multipliers in continuous vector-valued function spaces. Bull. Aust. Math. Soc. 46, 199–204 (1992)
Helemskii, AYa.: Helemskii, Banach and Locally Convex Algebras. Clarendon Press, Oxford (1993)
Husain, T.: Multipliers of topological algebras. Diss. Math. 285, 1–36 (1989)
Johnson, B.E.: An introduction to the theory of centralizers. Proc. Lond. Math. Soc. 14, 299–320 (1964)
Johnson, B.E.: Continuity of centralisers on Banach algebras. J. Lond. Math. Soc. 41, 639–640 (1966)
Katsaras, A.K.: On the strict topology in the non-locally convex setting. Math. Nachr. 102, 321–329 (1981)
Khan, L.A.: Some approximation results for the compact-open topology. Period. Math. Hung. 30, 81–86 (1995)
Khan, L.A.: Topological modules of continuous homomorphisms. J. Math. Anal. Appl. 343, 141–150 (2008)
Khan, L.A., Mohammad, N., Thaheem, A.B.: Double multipliers on topological algebras. Int. J. Math. Math. Sci. 22, 629–636 (1999)
Köthe, G.: Topological Vector Spaces I. Springer, New York (1969)
Lai, H.C.: Multipliers of a Banach algebra in the second conjugate algebra as an idealizer. Tohoku Math. J. 26, 431–452 (1974)
Lai, H.C.: Multipliers for some spaces of Banach algebra valued functions. Rocky Mt. J. Math. 15, 157–166 (1985)
Larson, R.: An Introduction to the Theory of Multipliers. Springer, New York (1971)
Mallios, A.: Topological Algebras—Selected Topics. North-Holland, Amsterdam (1986)
Rolewicz, S.: Metric Linear Spaces. D. Reidel Publishing Company, Warszawa (1985)
Shuchat, A.H.: Approximation of vector-valued continuous functions. Proc. Am. Math. Soc. 31, 97–103 (1972)
Wang, J.K.: Multipliers of commutative Banach algebras. Pac. J. Math. 11, 1131–1149 (1961)
Żelazko, W.: Metric generalizations of Banach algebras. Diss. Math. 47, 1–70 (1965)
Żelazko, W.: Banach Algebras. Elsevier, Amsterdam (1973)
Acknowledgments
This work has been done under the Project No. 3-059/429. The authors are grateful to the Deanship of Scientific Research of the King Abdulaziz University, Jeddah, for their financial support.
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Communicated by Rosihan M. Ali, Dato’.
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Khan, L.A., Alsulami, S.M. Multipliers of Commutative \(\varvec{F}\)-Algebras of Continuous Vector-Valued Functions. Bull. Malays. Math. Sci. Soc. 38, 345–358 (2015). https://doi.org/10.1007/s40840-014-0022-z
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DOI: https://doi.org/10.1007/s40840-014-0022-z