Automatic continuity on continuous inverse algebras

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University, Iran

10.22072/wala.2022.539443.1347

Abstract

    In this paper, we first investigate the continuity of the spectral radius functions on continuous inverse algebras. Then we support our results by some examples. Finally, we continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms on these algebras.

Keywords


[1] B. Aupetit, A Primer on Spectral Theory, Springer-Verlag, 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] L. Burlando, Continuity of spectrum and spectral radius in Banach algebras, Functional Analysis and Operator Theory, 
      Banach Center Publ., Institute of Mathematics, Polish Academy of Sciences, Warszawa, 30, (1994), 53-100.
[5] H.G. Dales, Banach Algebras and Automatic Continuity}, Clarendon Press, Oxford, 2000.
[6] T. Ghasemi Honary and M. Najafi Tavani, Upper semicontinuity of the spectrum function and automatic continuity in 
      topological $Q$-algebras, Note Mat., 28(2), (2008), 57-62. 
[7] H. Goldmann, Uniform Frechet Algebras}, North-Holland, 1990.
[8] T. Husain, Multiplicative Functionals on Topological Algebras, Research notes in Math. 85, Pitmann Publishing, Boston,  
      1983.
[9] B.E. Johnson, The uniqueness of the complete norm topology, Bull. Am. Math. Soc., 73, (1967), 537-539.
[10] A. Mallios, Topological Algebras: Selected Topics, North-Holland, Amsterdam, 1986.
[11] A. Naziri-Kordkadi, Topics on continuous inverse algebras, J. Algebr. Syst., 9}(2), (2022), 219-227. 
[12] 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.
[13] J.D. Newburgh, The variation of spectra, Duke Math. J., 18, (1951), 165-176. 
[14] W. Rudin, Functional Analysis, McGraw- Hill, 1973.