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A Carlson type inequality with blocks and interpolation

Natan Kruglyak, Lech Maligranda, Lars Persson (1993)

Studia Mathematica

An inequality, which generalizes and unifies some recently proved Carlson type inequalities, is proved. The inequality contains a certain number of “blocks” and it is shown that these blocks are, in a sense, optimal and cannot be removed or essentially changed. The proof is based on a special equivalent representation of a concave function (see [6, pp. 320-325]). Our Carlson type inequality is used to characterize Peetre’s interpolation functor ⟨ ⟩ φ (see [26]) and its Gagliardo closure on couples of...

A class of locally convex spaces without 𝒞 -webs

Manuel Valdivia (1982)

Annales de l'institut Fourier

In this article we give some properties of the tensor product, with the ϵ and π topologies, of two locally convex spaces. As a consequence we prove that the theory of M. de Wilde of the closed graph theorem does not contain the closed graph theorem of L. Schwartz.

A commutator theorem with applications.

Mario Milman (1993)

Collectanea Mathematica

We give an extension of the commutator theorems of Jawerth, Rochberg and Weiss [9] for the real method of interpolation. The results are motivated by recent work by Iwaniek and Sbordone [6] on generalized Hodge decompositions. The main estimates of these authors are based on a commutator theorem for a specific operator acting on Lp spaces and through the use of the complex method of interpolation. In this note we give an extension of the Iwaniek-Sbordone theorem to general real interpolation scales....

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 lifting theorem for locally convex subspaces of L 0

R. Faber (1995)

Studia Mathematica

We prove that for every closed locally convex subspace E of L 0 and for any continuous linear operator T from L 0 to L 0 / E there is a continuous linear operator S from L 0 to L 0 such that T = QS where Q is the quotient map from L 0 to L 0 / E .

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