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 ...

While the article was in publication process, we found a mistake in a key tool for the proof one of the main results. As a consequence, our result on the ball Au(BX) algebra remains open. For the algebra Hb(X) we obtain a ...

The Cluster Value Theorem is known for being a weak version of the classical Corona Theorem. Given a Banach space X, we study the Cluster Value Problem for the ball algebra Au(BX), the Banach algebra of all uniformly ...

We study the spectrum Mb(U) of the algebra of bounded-type holomorphic functions on a complete Reinhardt domain in a symmetrically regular Banach space E as an analytic manifold over the bidual of the space. In the case ...

Under certain hypotheses on the Banach space X, we prove that the set of analytic functions in Au(X) (the algebra of all holomorphic and uniformly continuous functions in the ball of X) whose Aron–Berner extensions attain ...