Displaying 141 – 160 of 394

Showing per page

On nonbornological barrelled spaces

Manuel Valdivia (1972)

Annales de l'institut Fourier

If E is the topological product of a non-countable family of barrelled spaces of non-nulle dimension, there exists an infinite number of non-bornological barrelled subspaces of E . The same result is obtained replacing “barrelled” by “quasi-barrelled”.

On non-primary Fréchet Schwartz spaces

J. Díaz (1997)

Studia Mathematica

Let E be a Fréchet Schwartz space with a continuous norm and with a finite-dimensional decomposition, and let F be any infinite-dimensional subspace of E. It is proved that E can be written as G ⨁ H where G and H do not contain any subspace isomorphic to F. In particular, E is not primary. If the subspace F is not normable then the statement holds for other quasinormable Fréchet spaces, e.g., if E is a quasinormable and locally normable Köthe sequence space, or if E is a space of holomorphic functions...

On operator ideals related to (p,σ)-absolutely continuous operators

J. López Molina, E. Sánchez Pérez (2000)

Studia Mathematica

We study tensor norms and operator ideals related to the ideal P p , σ , 1 < p < ∞, 0 < σ < 1, of (p,σ)-absolutely continuous operators of Matter. If α is the tensor norm associated with P p , σ (in the sense of Defant and Floret), we characterize the ( α ' ) t -nuclear and ( α ' ) t - integral operators by factorizations by means of the composition of the inclusion map L r ( μ ) L 1 ( μ ) + L p ( μ ) with a diagonal operator B w : L ( μ ) L r ( μ ) , where r is the conjugate exponent of p’/(1-σ). As an application we study the reflexivity of the components of the ideal...

On prequojections and their duals.

M. I. Ostrovskii (1998)

Revista Matemática Complutense

The paper is devoted to the class of Fréchet spaces which are called prequojections. This class appeared in a natural way in the structure theory of Fréchet spaces. The structure of prequojections was studied by G. Metafune and V. B. Moscatelli, who also gave a survey of the subject. Answering a question of these authors we show that their result on duals of prequojections cannot be generalized from the separable case to the case of spaces of arbitrary cardinality. We also introduce a special class...

Currently displaying 141 – 160 of 394