Gleason parts for algebras of holomorphic functions in infinite dimensions

被引：7

作者：

Aron, Richard M. ^{[1
]}

Dimant, Veronica ^{[2
,3
]}

Lassalle, Silvia ^{[2
,3
]}

Maestre, Manuel ^{[4
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Univ San Andres, Dept Matemat & Ciencias, Vito Dumas 284,B1644BID, Victoria, Buenos Aires, Argentina

[3] Consejo Nacl Invest Cient & Tecn, Buenos Aires, DF, Argentina

[4] Univ Valencia, Dept Anal Matemat, Doctor Moliner 50, E-46100 Valencia, Spain

来源：

REVISTA MATEMATICA COMPLUTENSE | 2020年 / 33卷 / 02期

关键词：

Gleason parts; Spectrum; Algebras of holomorphic functions; Bounded analytic functions; ANALYTIC-FUNCTIONS; THEOREM; FIBERS; BALL;

D O I：

10.1007/s13163-019-00324-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a complex Banach space X with open unit ball BX, consider the Banach algebras H8 ( BX) of bounded scalar-valued holomorphic functions and the subalgebra Au( BX) of uniformly continuous functions on BX. Denoting either algebra by A, we study the Gleason parts of the set of scalar-valued homomorphismsM(A) on A. Following remarks on the general situation, we focus on the case X = c0, giving a complete characterization of the Gleason parts of M(Au( Bc0)) and, among other things, showing that every fiber inM(H8 ( Bc0)) over a point in B 8 contains 2c discs lying in different Gleason parts.

引用

页码：415 / 436

页数：22

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