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Projective descriptions of the (LF)-spaces of type LB(λp(A), F)

Part of: Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

Angela A. Albanese
Angela A. Albanese
Affiliation:
Dipartimento di Matematica ‘E. De Giorgi’ Università di Lecce, C.P. 193 Via Per Arnesano 73100 LecceItaly e-mail: albanese@ilenic.unile.it
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Abstract

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Let 1 < p < + ∞ or p = 0 and let A = (an)n be an increasing sequence of strictly positive weights on I. Let F be a Fréchet space. It is proved that if λp(A) satisfies the density condition of Heinrich and a certain condition (Ct) holds, then the (LF)-space LBi(λp(A), F) is a topological subspace of Lb(λp(A), F). It is also proved that these conditions are necessary provided F = λq(A) or F contains a complemented copy of Iq with 1 < p ≤ q < +∞.

Keywords

spaces of linear continuous maps, echelon and co-echelon spaces of order p, projective description

MSC classification

Secondary: 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.) 46A32: Spaces of linear operators; topological tensor products; approximation properties 46A45: Sequence spaces (including Köthe sequence spaces)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 2 , October 2003 , pp. 163 - 180
Copyright
Copyright © Australian Mathematical Society 2003

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