Topological algebras with subadditive boundedness radius
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M. Sabet
sabet.majid@gmail.com
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R. G. Sanati
reza_sanaaty@yahoo.com
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DOI:
https://doi.org/10.4067/S0719-06462020000300289Abstract
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
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