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Nearness relations in linear spaces

Martin Kalina (2004)

Kybernetika

In this paper, we consider nearness-based convergence in a linear space, where the coordinatewise given nearness relations are aggregated using weighted pseudo-arithmetic and geometric means and using continuous t-norms.

Nevanlinna algebras

A. Haldimann, H. Jarchow (2001)

Studia Mathematica

The Nevanlinna algebras, α p , of this paper are the L p variants of classical weighted area Nevanlinna classes of analytic functions on = z ∈ ℂ: |z| < 1. They are F-algebras, neither locally bounded nor locally convex, with a rich duality structure. For s = (α+2)/p, the algebra F s of analytic functions f: → ℂ such that ( 1 - | z | ) s | f ( z ) | 0 as |z| → 1 is the Fréchet envelope of α p . The corresponding algebra s of analytic f: → ℂ such that s u p z ( 1 - | z | ) s | f ( z ) | < is a complete metric space but fails to be a topological vector space. F s is also...

Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces

M. Jimenéz Sevilla, Rafael Payá (1998)

Studia Mathematica

For each natural number N, we give an example of a Banach space X such that the set of norm attaining N-linear forms is dense in the space of all continuous N-linear forms on X, but there are continuous (N+1)-linear forms on X which cannot be approximated by norm attaining (N+1)-linear forms. Actually,X is the canonical predual of a suitable Lorentz sequence space. We also get the analogous result for homogeneous polynomials.

Normed barrelled spaces

Christopher Stuart (2000)

Banach Center Publications

In this paper we present a general “gliding hump” condition that implies the barrelledness of a normed vector space. Several examples of subspaces of l 1 are shown to be barrelled using the theorem. The barrelledness of the space of Pettis integrable functions is also implied by the theorem (this was first shown in [3]).

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