A Free Convenient Vector Space for Holomorphic Spaces.
Let be a complex Banach space. Recall that admits afinite-dimensional Schauder decompositionif there exists a sequence of finite-dimensional subspaces of such that every has a unique representation of the form with for every The finite-dimensional Schauder decomposition is said to beunconditionalif, for every the series which represents converges unconditionally, that is, converges for every permutation of the integers. For short, we say that admits an unconditional F.D.D.We...
We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H.We deal with the problem by cutting with a family of complex hyperplanes and applying the already known result for the compact case.
Let be a continuous map of the closure of the open unit disc of into a unital associative Banach algebra , whose restriction to is holomorphic, and which satisfies the condition whereby for all and whenever (where is the spectrum of any ). One of the basic results of the present paper is that is , that is to say, is then a compact subset of that does not depend on for all . This fact will be applied to holomorphic self-maps of the open unit ball of some -algebra...
We present several characterizations and representations of semi-complete vector fields on the open unit balls in complex Euclidean and Hilbert spaces.
In finite-dimensional complex analysis, the extension of holomorphic maps has been investigated by many authors. In recent years some authors have considered this problem in the infinite-dimensional case. The aim of the present note is to study the extension of holomorphic maps with values in some Banach complex manifolds.