\(\varphi\)-multipliers on Banach algebras and topological modules. (English) Zbl 1350.46035

Adib, Marjan

Abstr. Appl. Anal. 2015, Article ID 951021, 6 p. (2015).

Summary: We prove some results concerning Arens regularity and amenability of the Banach algebra \(M_\varphi (A)\) of all \(\varphi\)-multipliers on a given Banach algebra \(A\). We also consider \(\varphi\)-multipliers in the general topological module setting and investigate some of their properties. We discuss the \(\varphi\)-strict and \(\varphi\)-uniform topologies on \(M_\varphi (A)\). A characterization of \(\varphi\)-multipliers on \(L_1 (G)\)-module \(L_p (G)\), where \(G\) is a compact group, is given.

MSC:

46H25	Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
47B48	Linear operators on Banach algebras

Keywords:

Arens regularity; amenability; \(\varphi\)-multipliers

References:

[1]	Helgason, S., Multipliers of Banach algebras, Annals of Mathematics, 64, 240-254, (1956) · Zbl 0072.32303
[2]	Wang, J.-K., Multipliers of commutative Banach algebras, Pacific Journal of Mathematics, 11, 1131-1149, (1961) · Zbl 0127.33302
[3]	Birtel, F. T., Isomorphisms and isometric multipliers, Proceedings of the American Mathematical Society, 13, 204-210, (1962) · Zbl 0117.09701
[4]	Riazi, A.; Adib, M., φ-multipliers on Banach algebras without order, International Journal of Mathematical Analysis, 3, 1–4, 121-132, (2009) · Zbl 1180.47026
[5]	Larsen, R., An Introduction to The Theory of Multipliers, (1970), New York, NY, USA: Springer, New York, NY, USA
[6]	Zalar, B., On centralizers of semiprime rings, Commentationes Mathematicae Universitatis Carolinae, 32, 4, 609-614, (1991) · Zbl 0746.16011
[7]	Vukman, J., An identity related to centralizers in semiprime rings, Commentationes Mathematicae Universitatis Carolinae, 40, 255-265, (2001)
[8]	Bonsall, F. F.; Duncan, J., Complete Normed Algebras, (1973), Berlin, Germany: Springer, Berlin, Germany · Zbl 0271.46039
[9]	Runde, V., Lectures on Amenability. Lectures on Amenability, Lecture Notes in Mathematics, 1774, (2002), Berlin, Germany: Springer, Berlin, Germany · Zbl 0999.46022
[10]	Johnson, B. E., An introduction to the theory of centralizers, Proceedings of the London Mathematical Society, 14, 299-320, (1964) · Zbl 0143.36102
[11]	Sentilles, F. D.; Taylor, D. C., Factorization in Banach algebras and the general strict topology, Transactions of the American Mathematical Society, 142, 141-152, (1969) · Zbl 0185.21103