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Products in almost f -algebras

Karim Boulabiar (2000)

Commentationes Mathematicae Universitatis Carolinae

Let A be a uniformly complete almost f -algebra and a natural number p { 3 , 4 , } . Then Π p ( A ) = { a 1 a p ; a k A , k = 1 , , p } is a uniformly complete semiprime f -algebra under the ordering and multiplication inherited from A with Σ p ( A ) = { a p ; 0 a A } as positive cone.

Projective representations of spaces of quasianalytic functionals

José Bonet, Reinhold Meise, Sergeĭ N. Melikhov (2004)

Studia Mathematica

The weighted inductive limit of Fréchet spaces of entire functions in N variables which is obtained as the Fourier-Laplace transform of the space of analytic functionals on an open convex subset of N can be described algebraically as the intersection of a family of weighted Banach spaces of entire functions. The corresponding result for the spaces of quasianalytic functionals is also derived.

Properties of Orlicz-Pettis or Nikodym type and barrelledness conditions

Philippe Turpin (1978)

Annales de l'institut Fourier

An Orlicz-Pettis type property for vector measures and also the “Uniform Boundedness Principle” are shown to fail without local convexity assumption. The author asks under which generalized convexity hypotheses these properties remain true. This problem is expressed in terms of barrelledness type conditions.

Pseudocomplémentation dans les espaces de Banach

Patric Rauch (1991)

Studia Mathematica

This paper introduces the following definition: a closed subspace Z of a Banach space E is pseudocomplemented in E if for every linear continuous operator u from Z to Z there is a linear continuous extension ū of u from E to E. For instance, every subspace complemented in E is pseudocomplemented in E. First, the pseudocomplemented hilbertian subspaces of L ¹ are characterized and, in L p with p in [1, + ∞[, classes of closed subspaces in which the notions of complementation and pseudocomplementation...

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