On the boundedness of almost multipliers on certain Banach algebras

Subject Areas : Operator theory

E. Ansari-Piri ¹ (Department of Pure Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran)
M. Shams Yousefi ² (Department of Pure Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran)
S. Nouri ³ (Department of Pure Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran)

Received: 2015-07-09 Accepted : 2015-11-05 Published : 2015-05-01

Keywords: Almost multipliers, almost additive maps, dual map, stable normed algebras,

Abstract :

Almost multiplier is rather a new concept in the theory of almost functions. In thispaper we discussion the boundedness of almost multipliers on some special Banach algebras,namely stable algebras. We also define an adjoint and extension for almost multiplier.

References:

[1] E. Ansari-Piri, S. Nouri, Almost multipliers and some of their properties, Preprint.

[2] E. Ansari-Piri, S. Nouri, Stable normed algebra, Priprint.

[3] F. Birtal, Isomorphism and isometric multipliers, Proc. Amer. Math. Soc. (1962), no. 13, 204-210.

[4] B. Host, F. Parreau, Sur un probleme de I. Glicksberg: les ideauxfermes de type ni deM(G), Ann. Inst. Fourier (Grenoble) 28(1978), no.3, 143-164.

[5] S. Helganson, Multipliers of Banach algebras, Ann. Math ,64 (1956), 240-254.

[6] R. Larsen, Theory of Multipliers, Springer, Berlin, 1971.

[7] K. B. Laursen, M. Mbekhta, Closed range multipliers and generalized inverses, Stud. Math. 107 (1993)126-135.

[8] T. Miura, G. Hirasawa, S. Takahasi, Stability of multipliers on Banach algebras, A.M.S. 45 (2004), 2377-2381.

[9] A. Ulger, Multipliers with closed range on commutative semsimple Banach algebras, Stud. Math. 153 (2002), no. 1, 59-80.

[10] J. Wang, Multipliers of commutative Banach algebras, Pacific J. Math, 11(1961), 1131-1149.

[11] Y. Zaiem, Operateurs de convolution d'image femee et unitesapproches, Bull. Sci. Math. 99 (1975), 65-74.