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Calculations in new sequence spaces

Bruno de Malafosse (2007)

Archivum Mathematicum

In this paper we define new sequence spaces using the concepts of strong summability and boundedness of index p > 0 of r -th order difference sequences. We establish sufficient conditions for these spaces to reduce to certain spaces of null and bounded sequences.

Cesàro wedge and weak Cesàro wedge F K -spaces

H. G. Ince (2002)

Czechoslovak Mathematical Journal

In this paper we deal with Cesàro wedge and weak Cesàro wedge F K -spaces, and give several characterizations. Some applications of these spaces to general summability domains are also studied.

Characterizing Fréchet-Schwartz spaces via power bounded operators

Angela A. Albanese, José Bonet, Werner J. Ricker (2014)

Studia Mathematica

We characterize Köthe echelon spaces (and, more generally, those Fréchet spaces with an unconditional basis) which are Schwartz, in terms of the convergence of the Cesàro means of power bounded operators defined on them. This complements similar known characterizations of reflexive and of Fréchet-Montel spaces with a basis. Every strongly convergent sequence of continuous linear operators on a Fréchet-Schwartz space does so in a special way. We single out this type of "rapid convergence" for a sequence...

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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