It is known that all k-homogeneous orthogonally additive polynomials P over C(K) are of the form P(x)= ∫Kxkdμ. Thus, x → xk factors all orthogonally additive polynomials through some linear form μ. We show that no such ...

We study the extension of holomorphic functions of bounded type defined on an open subset of a Banach space to larger domains. For this, we first characterize the envelope of holomorphy of a Riemann domain over a Banach ...

Given A a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, HbA(E). We prove that, under very natural conditions satisfied by many usual classes of ...

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 ...

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 ...

For two complex Banach spaces and , in this paper, we study the generalized spectrum M(, ) of all nonzero algebra homomorphisms from H(), the algebra of all bounded type entire functions on , into H(). We endow M(, ) with ...