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Approximation of holomorphic functions in Banach spaces admitting a Schauder decomposition

Francine Meylan (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let X be a complex Banach space. Recall that X admits afinite-dimensional Schauder decompositionif there exists a sequence { X n } n = 1 of finite-dimensional subspaces of X , such that every x X has a unique representation of the form x = n = 1 x n , with x n X n for every n . The finite-dimensional Schauder decomposition is said to beunconditionalif, for every x X , the series x = n = 1 x n , which represents x , converges unconditionally, that is, n = 1 x π ( n ) converges for every permutation π of the integers. For short, we say that X admits an unconditional F.D.D.We...

Non compact boundaries of complex analytic varieties in Hilbert spaces

Samuele Mongodi, Alberto Saracco (2014)

Complex Manifolds

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.

On a class of inner maps

Edoardo Vesentini (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let f be a continuous map of the closure Δ ¯ of the open unit disc Δ of C into a unital associative Banach algebra A , whose restriction to Δ is holomorphic, and which satisfies the condition whereby 0 σ f z Δ ¯ for all z Δ and σ f z Δ whenever z Δ (where σ x is the spectrum of any x A ). One of the basic results of the present paper is that f is , that is to say, σ f z is then a compact subset of Δ that does not depend on z for all z Δ ¯ . This fact will be applied to holomorphic self-maps of the open unit ball of some J * -algebra...

Some remarks on holomorphic extension in infinite dimensions

Pham Ban (1994)

Colloquium Mathematicae

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.

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