Displaying similar documents to “Approximation of holomorphic mappings on infinite dimensional spaces.”

The fixed points of holomorphic maps on a convex domain

Do Duc Thai (1992)

Annales Polonici Mathematici

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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.

p-Envelopes of non-locally convex F-spaces

C. M. Eoff (1992)

Annales Polonici Mathematici

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The p-envelope of an F-space is the p-convex analogue of the Fréchet envelope. We show that if an F-space is locally bounded (i.e., a quasi-Banach space) with separating dual, then the p-envelope coincides with the Banach envelope only if the space is already locally convex. By contrast, we give examples of F-spaces with are not locally bounded nor locally convex for which the p-envelope and the Fréchet envelope are the same.

Some remarks on the space of differences of sublinear functions

Sven Bartels, Diethard Pallaschke (1994)

Applicationes Mathematicae

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Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel...

A generalization of the Hahn-Banach theorem

Jolanta Plewnia (1993)

Annales Polonici Mathematici

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If C is a non-empty convex subset of a real linear space E, p: E → ℝ is a sublinear function and f:C → ℝ is concave and such that f ≤ p on C, then there exists a linear function g:E → ℝ such that g ≤ p on E and f ≤ g on C. In this result of Hirano, Komiya and Takahashi we replace the sublinearity of p by convexity.

Factorization of uniformly holomorphic functions

Luiza A. Moraes, Otilia W. Paques, M. Carmelina F. Zaine (1995)

Annales Polonici Mathematici

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Let E be a complex Hausdorff locally convex space such that the strong dual E’ of E is sequentially complete, let F be a closed linear subspace of E and let U be a uniformly open subset of E. We denote by Π: E → E/F the canonical quotient mapping. In §1 we study the factorization of uniformly holomorphic functions through π. In §2 we study F-quotients of uniform type and introduce the concept of envelope of uF-holomorphy of a connected uniformly open subset U of E. The main result states...