Document Type : Original Manuscript

Author

Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.

Abstract

In this paper, we first provide some counterexamples and derive some new results concerning the usual and singular spec- trum of an element in continuous inverse algebras. Then we continue our investigation about the characterizations of multiplicative linear maps and their related results in these algebras.

Keywords

1. B. Aupetit, A Primer on Spectral Theory, Springer-Verlage, 1991.
2. V. K. Balachandran,Topological Algebras, New York, Elsevier, 2000.
3. H. Biller, Continuous inverse algebras with involution, Forum Math., 22(6) (2010), 1033–1059.
4. F. F. Bonsal and J. Doncan, Complete Normed Algebras, Springer-Verlag, Berlin, 1973.
5. M. Fragoulopoulou, Topological Algebras with Involution, Elsevier, 2005.
6. M. Luczak, On the Gleason-Kahane-Zelazko theorem, Comment. Math. Prace Mat., 44(2) (2004), 245–253.
7. E. Michael, Locally multiplicatively convex topological algebras, Mem. Amer. Math. Soc., vol. 11, Amer. Math. Soc, Providence, RI, 1952.
8. A. Naziri-Kordkandi, A. Zohri, F. Ershad, and B. Yousefi, A class of new results in FLM Algebras, SCMA, 13(1) (2019), 93–100.
9. A. Naziri-Kordkandi, A. Zohri, F. Ershad, and B. Yousefi, Continuity in Fundamental Locally multiplicative topological Algebras, Int. J. Nonlinear Anal. Appl., 12(1) (2021), 129–141.
10. C. Swartz, An Introduction to Functional Analysis, Marcel Dekker, Inc. New York, 1992.
11. P. Turpin, Une remarque sur les algebres a inverse continu., C. R. Acad. Sci. Paris Ser. A-B, 270 (1970), A1686 -A1689.
12. W. Zelazko, Concerning entire functions in B0-algebras, Studia Math., 110(3) (1994), 283–290.