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A construction of simplicial objects

Tomáš Crhák (2001)

Commentationes Mathematicae Universitatis Carolinae

We construct a simplicial locally convex algebra, whose weak dual is the standard cosimplicial topological space. The construction is carried out in a purely categorical way, so that it can be used to construct (co)simplicial objects in a variety of categories --- in particular, the standard cosimplicial topological space can be produced.

A Lifting Result for Locally Pseudo-Convex Subspaces of L₀

Félix Cabello Sánchez (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

It is shown that if F is a topological vector space containing a complete, locally pseudo-convex subspace E such that F/E = L₀ then E is complemented in F and so F = E⊕ L₀. This generalizes results by Kalton and Peck and Faber.

A splitting theory for the space of distributions

P. Domański, D. Vogt (2000)

Studia Mathematica

The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'

An additivity formula for the strict global dimension of C(Ω)

Seytek Tabaldyev (2014)

Open Mathematics

Let A be a unital strict Banach algebra, and let K + be the one-point compactification of a discrete topological space K. Denote by the weak tensor product of the algebra A and C(K +), the algebra of continuous functions on K +. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension is equal to .

Banach spaces, à la recherche du temps perdu.

Jesús M. Fernández Castillo (2000)

Extracta Mathematicae

What follows is the opening conference of the late night seminar at the III Conference on Banach Spaces held at Jarandilla de la Vera, Cáceres. Maybe the reader should not take everything what follows too seriously: after all, it was designed for a friendly seminar, late in the night, talking about things around a table shared by whisky, preprints and almonds. Maybe the reader should not completely discard it. Be as it may, it seems to me by now that everything arrives in the nick of time. A twisted...

Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives

Paweł Domański (2004)

Banach Center Publications

This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Poznań, 2003). It contains a brief survey of applications to classical problems of analysis of the theory of the so-called PLS-spaces (in particular, spaces of distributions and real analytic functions). Sequential representations of the spaces and the theory of the functor Proj¹ are applied to questions like solvability of linear partial differential equations, existence of a solution depending...

Homological dimensions and approximate contractibility for Köthe algebras

Alexei Yu. Pirkovskii (2010)

Banach Center Publications

We give a survey of our recent results on homological properties of Köthe algebras, with an emphasis on biprojectivity, biflatness, and homological dimension. Some new results on the approximate contractibility of Köthe algebras are also presented.

Ideals of extendable and liftable operators.

Pawel Domanski (2003)


Se introducen los ideales de operadores que admiten extensión o levantamiento y se presenta una nueva aproximación al estudio de la escisión de sucesiones exactas cortas de espacios de Banach. Se considera la maximalidad de estos ideales y se investiga si son cerrados respecto de los límites puntuales acotados. Se resumen algunos ejemplos y se clarifica el papel de los espacios L1 y L∞.

On (Co)homology of triangular Banach algebras

Mohammad Sal Moslehian (2005)

Banach Center Publications

Suppose that A and B are unital Banach algebras with units 1 A and 1 B , respectively, M is a unital Banach A,B-module, = A M 0 B is the triangular Banach algebra, X is a unital -bimodule, X A A = 1 A X 1 A , X B B = 1 B X 1 B , X A B = 1 A X 1 B and X B A = 1 B X 1 A . Applying two nice long exact sequences related to A, B, , X, X A A , X B B , X A B and X B A we establish some results on (co)homology of triangular Banach algebras.

On Lindenstrauss-Pełczyński spaces

Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez (2006)

Studia Mathematica

We consider some stability aspects of the classical problem of extension of C(K)-valued operators. We introduce the class ℒ of Banach spaces of Lindenstrauss-Pełczyński type as those such that every operator from a subspace of c₀ into them can be extended to c₀. We show that all ℒ-spaces are of type but not conversely. Moreover, -spaces will be characterized as those spaces E such that E-valued operators from w*(l₁,c₀)-closed subspaces of l₁ extend to l₁. Regarding examples we will show that...

On the derived tensor product functors for (DF)- and Fréchet spaces

Oğuz Varol (2007)

Studia Mathematica

For a (DF)-space E and a tensor norm α we investigate the derivatives T o r α l ( E , · ) of the tensor product functor E ̃ α · : from the category of Fréchet spaces to the category of linear spaces. Necessary and sufficient conditions for the vanishing of T o r ¹ α ( E , F ) , which is strongly related to the exactness of tensored sequences, are presented and characterizations in the nuclear and (co-)echelon cases are given.

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