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On the -characteristic of fractional powers of linear operators

Jürgen Appell, Marilda A. Simões, Petr P. Zabrejko (1994)

Commentationes Mathematicae Universitatis Carolinae

We describe the geometric structure of the -characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss- Ovchinnikov interpolation theorems, as well as on the Krasnosel’skij-Krejn factorization theorem.

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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