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On complete, precompact and compact sets.

Leonhard Frerick (1993)

Collectanea Mathematica

Completeness criterion of W. Robertson is generalized. Applications to vector valued sequences and to spaces of linear mappings are given.

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 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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