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The bidual of a tensor product of Banach spaces.

Félix Cabello Sánchez, Ricardo García (2005)

Revista Matemática Iberoamericana

This paper studies the relationship between the bidual of the (projective) tensor product of Banach spaces and the tensor product of their biduals.

The Cauchy-Riemann equations in infinite dimensions

László Lempert (1998)

Journées équations aux dérivées partielles

I will explain basic concepts/problems of complex analysis in infinite dimensions, and survey the few approaches that are available to solve those problems.

The density property for JB*-triples

Seán Dineen, Michael Mackey, Pauline Mellon (1999)

Studia Mathematica

We obtain conditions on a JB*-algebra X so that the canonical embedding of X into its associated quasi-invertible manifold has dense range. We prove that if a JB* has this density property then the quasi-invertible manifold is homogeneous for biholomorphic mappings. Explicit formulae for the biholomorphic mappings are also given.

The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of C * -algebras

Kazimierz Włodarczyk (1994)

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

The aim of this paper is to start a systematic investigation of the existence of angular limits and angular derivatives of holomorphic maps of infinite dimensional Siegel domains in J * -algebras. Since J * -algebras are natural generalizations of C * -algebras, B * -algebras, J ⁢ C * -algebras, ternary algebras and complex Hilbert spaces, various significant results follow. Examples are given.

The fixed points of holomorphic maps on a convex domain

Do Duc Thai (1992)

Annales Polonici Mathematici

We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in ℂ n then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.

The Oka-Weil theorem in topological vector spaces

Bui Dac Tac (1991)

Annales Polonici Mathematici

It is shown that a sequentially complete topological vector space X with a compact Schauder basis has WSPAP (see Definition 2) if and only if X has a pseudo-homogeneous norm bounded on every compact subset of X.

The symmetric tensor product of a direct sum of locally convex spaces

José Ansemil, Klaus Floret (1998)

Studia Mathematica

An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for ⨂ τ , s n ( F 1 ⨁ F 2 ) gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective “full” tensor product of a locally convex space E are isomorphic if E is isomorphic to its square E 2 .

The theorems of Glicksberg and Hurwitz for holomorphic maps in complex Banach spaces

Kazimier Wzodarczyk (1993)

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

General versions of Glicksberg's theorem concerning zeros of holomorphic maps and of Hurwitz's theorem on sequences of analytic functions is extended to infinite dimensional Banach spaces.

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