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- W2156965648 abstract "A complex Banach algebra X with an identity element~ e~ is reducible if~ and only if, X contains a proper bilateral ideal different from zero, which is a Banach subalgebra with an identity element. A necessary and sufficient condition for X to be reducible is that its center contain an idempotent different from 0 and from e [3, p. 176]. In [4] E. R. Lorch has shown that a commutative Banach algebra X with an identity element is irreducible if, and only if, the exponential is simply periodic on X. In the present paper we will investigate the validity of the above statement for arbitrary entire functions on arbitrary Banach algebras. The main result will be the following" @default.
- W2156965648 created "2016-06-24" @default.
- W2156965648 creator A5051340922 @default.
- W2156965648 date "1970-01-01" @default.
- W2156965648 modified "2023-10-02" @default.
- W2156965648 title "Periodic entire functions and reducible Banach algebras" @default.
- W2156965648 cites W2049455760 @default.
- W2156965648 doi "https://doi.org/10.1007/bfb0060326" @default.
- W2156965648 hasPublicationYear "1970" @default.
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