info:eu-repo/semantics/article
Gleason parts for algebras of holomorphic functions in infinite dimensions
Fecha
2019-09Registro en:
Aron, Richard Martin; Dimant, Veronica Isabel; Lassalle, Silvia Beatriz; Maestre, Manuel; Gleason parts for algebras of holomorphic functions in infinite dimensions; Springer; Revista Matematica Complutense; 33; 2; 9-2019; 415-436
1139-1138
CONICET Digital
CONICET
Autor
Aron, Richard Martin
Dimant, Veronica Isabel
Lassalle, Silvia Beatriz
Maestre, Manuel
Resumen
For a complex Banach space X with open unit ball BX, consider the Banach algebras H∞(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 homomorphisms M(A) on A. Following remarks on the general situation, we focus on the case X= c, giving a complete characterization of the Gleason parts of M(Au(Bc0)) and, among other things, showing that every fiber in M(H∞(Bc0)) over a point in Bℓ∞ contains 2 c discs lying in different Gleason parts.