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Extension and splitting theorems for Fréchet spaces of type 2.

A. Defant; P. Domanski; M. Mastylo — 1999

Revista Matemática Complutense

We prove the following common generalization of Maurey's extension theorem and Vogt's (DN)-(Omega) splitting theorem for Fréchet spaces: if T is an operator from a subspace E of a Fréchet space G of type 2 to a Fréchet space F of dual type 2, then T extends to a map from G into F'' whenever G/E satisfies (DN) and F satisfies (Omega).

Coincidence of topologies on tensor products of Köthe echelon spaces

J. Bonet; A. Defant; A. Peris; M. Ramanujan — 1994

Studia Mathematica

We investigate conditions under which the projective and the injective topologies coincide on the tensor product of two Köthe echelon or coechelon spaces. A major tool in the proof is the characterization of the επ-continuity of the tensor product of two diagonal operators from $l_{p}$ to $l_{q}$ . Several sharp forms of this result are also included.

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