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Localization of bounded sets in tensor products.

A. Peris; M. J. Rivera — 1996

Revista Matemática de la Universidad Complutense de Madrid

The problem of topologies of Grothendieck is considered for complete tensor products of Fréchet spaces endowed with the topology defined by an arbitrary tensor norm. Some consequences on the stability of certain locally convex properties in spaces of operators are also given.

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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