6533b823fe1ef96bd127e22d

RESEARCH PRODUCT

Cluster values of holomorphic functions of bounded type

Richard M. AronDaniel CarandoSilvia LassalleManuel Maestre

subject

Discrete mathematicsSPECTRUMPure mathematicsMatemáticasApplied MathematicsGeneral MathematicsHolomorphic functional calculusHolomorphic functionFIBERBounded deformationBounded mean oscillationMatemática PuraBounded operatorANALYTIC FUNCTIONS OF BOUNDED TYPEBANACH SPACEBergman spaceBounded functionBounded inverse theoremCLUSTER VALUECIENCIAS NATURALES Y EXACTASMathematics

description

We study the cluster value theorem for Hb(X), the Fréchet algebra of holomorphic functions bounded on bounded sets of X. We also describe the (size of) fibers of the spectrum of Hb(X). Our results are rather complete whenever X has an unconditional shrinking basis and for X = ℓ1. As a byproduct, we obtain results on the spectrum of the algebra of all uniformly continuous holomorphic functions on the ball of ℓ1. Fil: Aron, Richard Martin. Kent State University; Estados Unidos Fil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina Fil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina Fil: Maestre, Manuel. Universidad de Valencia; España

yearjournalcountryeditionlanguage
2015-07-01Transactions of the American Mathematical Society
https://doi.org/10.1090/tran/6407