A multiplicative convolution on the spectra of algebras of symmetric analytic functions
Let \(H_{bs}(l_p)\) denote the algebra of all symmetric analytic functions on \(l_p\) that are bounded on bounded sets endowed with the topology of the uniform convergence on the bounded sets and by \(M_{bs}(l_p)\) the spectrum of \(H_{bs}(l_p)\), that is, the set of all non-zero continuous complex-valued homomorphisms. In [J. Math. Anal. Appl. 395, No.~2, 569--577 (2012; Zbl 1258.46021)], the authors defined a symmetric convolution operation in \(M_{bs}(l_p)\) which made it possible to obtain a representation of \(M_{bs}(l_1)\) in terms of entire functions of exponential type. It was then unknown to the authors whether this representation is onto. In the paper under review, they introduce a multiplicative convolution operation in \(M_{bs}(l_1)\) that allows them to show that such a representation is not onto.
polynomials and analytic functions on Banach spaces
scientific article; zbMATH DE number 6347549