The convolution operation on the spectra of algebras of symmetric analytic functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

Article

Chernega, Irina²  Galindo, Pablo¹  Zagorodnyuk, Andriy³ 

[1] Univ Valencia, Dept Anal Matemat, Burjassot 46100, Valencia, Spain

[2] Ukrainian Acad Sci, Inst Appl Problems Mech & Math, UA-79060 Lvov, Ukraine

[3] Vasyl Stefanyk Precarpathian Natl Univ, UA-76000 Ivano Frankvisk, Ukraine

关键词: Polynomials and analytic functions on Banach spaces;    Symmetric polynomials;    Spectra of algebras;    Entire functions of exponential type;   

DOI  :  10.1016/j.jmaa.2012.04.087

来源: Elsevier

【 摘 要 】

We show that the spectrum of the algebra of bounded symmetric analytic functions on l(p), 1 <= p < + infinity with the symmetric convolution operation is a commutative semigroup with the cancellation law for which we discuss the existence of inverses. For p = 1, a representation of the spectrum in terms of entire functions of exponential type is obtained which allows us to determine the invertible elements. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free