Topological algebras with subadditive boundedness radius

M. Sabet; R. G. Sanati

doi:10.4067/S0719-06462020000300289

DOI:

https://doi.org/10.4067/S0719-06462020000300289

Abstract

Let \(A\) be a topological algebra and \(\beta\) a subadditive boundedness radius on \(A\). In this paper we show that \(\beta\) is, under certain conditions, automatically submultiplicative. Then we apply this fact to prove that the spectrum of any element of \(A\) is non-empty. Finally, in the case when \(A\) is a normed algebra, we compare the initial normed topology with the normed topology \(\tau_{\beta}\), induced by \(\beta\) on \(A\), where \(\beta^{-1} (0)=0\).

Keywords

Topological algebra , strongly sequential algebra , boundedness radius

M. Sabet Department of Mathematics, Payame Noor University, Tehran, Iran.
R. G. Sanati Institute of Higher Education of ACECR (Academic Center of Education and Culture Research), Rasht branch, Iran.

Pages: 289–297
Date Published: 2020-12-07
Vol. 22 No. 3 (2020)

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