Cluster Values of Analytic Functions on a Banach Space

ARON R., CARANDO D., GAMELIN T.W., LASSALLE S., MAESTRE M.

MATHEMATISCHE ANNALEN

SPRINGER

Año: 2012 vol. 353 p. 293 - 303

0025-5831

We investigate uniform algebras of bounded analytic functions on the unit ball of a complex Banach space. We prove several cluster value theorems, relating cluster sets of a function to its range on the fibers of the spectrum of the algebra. These lead to weak versions of the corona theorem for l2 and for c0. In the case of the open unit ball of c0, we solve the corona problem whenever all but one of the functions comprising the corona data are uniformly approximable by polynomials in functions in the dual of c_0.