Document Type : Research Paper


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


In this paper, we first generalize the Gelfand-Mazur theorem for pseudo-Michael $Q$-algebras. Then some applications of the spectral mapping theorem are also investigated in $k$-Banach algebras.


Main Subjects

[1] B. Aupetit, A Primer on Spectral Theory, Springer-Verlage, 1991.
[2] V. K. Balachandran, Topological Algebras, North-Holland Math. Studies 185, Elsevier, Amsterdam, 2000.
[3] H. G. Dales, Banach Algebras and Automatic Continuity, Clarendon Press, Oxford, 2000.
[4] M. Fragoulopoulou, Topological Algebras with Involution, Elsevier, 2005.
[5] A. Mallios, Topological Algebras. Selected Topics, North-Holland, Amsterdam, 1986.
[6] E. Michael, Locally multiplicatively convex topological algebras. mem. Amer. Math. Soc. Vol. 11. Amer. Math. Soc. Providence, R1.1952.
[7] A. Naziri-Kordkandi, A. Zohri, F. Ershad, B.Yousefi, Continuity in Fundamental Locally multiplicative topological Algebras, Int. J. Nonlinear Anal. Appl. 12 (1) (2021),129-141.
[8] M. Ruzhansky, V. Turunen, Pseudo-Differential operators and Symmetries, Background Analysis and Advanced Topics Birkhauser, Basel, 2010.
[9] Z. Wang, J. Chen, Pseudo-Drazin inverses in associative rings and Banach alebras, Linear. Algebra. Appl. 437 (2012), 1332-1345.