On the spectra of algebras of analytic functions - Contemporary Mathematics

DANIEL CARANDO; DOMINGO GARCÍA; MANUEL MAESTRE; PABLO SEVILLA PERIS

Topics in complex analysis and operator theory

American Mathematical Society

Año: 2012; p. 165 - 198

In this paper we survey the most relevant recent developments on the research of the spectra of algebras of analytic functions. Weconcentrate  mainly in three algebras, the Banach algebra $H^infty(B)$  of all  boundedholomorphic functions on the unit ball $B$  of a complex Banach space $X$,  the Banach algebraof the ball $A_u(B)$, and  the Fr´{e}chet algebra $H_b(X)$ of all entire functions  bounded onbounded sets.