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Barrelled subspaces of spaces with subseries decompositions or Boolean rings of projections

Published online by Cambridge University Press:  18 May 2009

Lech Drewnowski ,
Miguel Florencio  and
Pedro J. Paúl
Lech Drewnowski
Affiliation:
Instytut Matematyki, Uniwertsytet A. Mickiewicza, Matejki 48-49, 60-769 Poznań, Poland Department of Mathematics, University of Mississippi, University MS38677, U.S.A. E-mail: DREWLECH@PLPUAM11.BITNET
Miguel Florencio
Affiliation:
E.S. Ingenieros Industriales, Avda Reina Mercedes S/N, 41012-Sevilla, Spain E-mail: PITI%ETSII.US.ES@CERNVAX and PITI%CICA.ES@CERNVAX
Pedro J. Paúl
Affiliation:
E.S. Ingenieros Industriales, Avda Reina Mercedes S/N, 41012-Sevilla, Spain E-mail: PITI%ETSII.US.ES@CERNVAX and PITI%CICA.ES@CERNVAX
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The research presented in this paper started by extending a theorem of Swetits [18]about barrelledness of subspaces of metrizable AK-spaces to general AK-spaces of scalar sequences. The extension reads as follows.

(1) A subspace λ0 of a barrelled AK-space λ such that λ0 ⊃ φ is barrelled if and only if its dualis weak* sequentially complete. If in addition λ0 is monotone, then it is barrelled if and only ifequals the Köthe dualof λ0.

As an easy consequence of this extension, we obtained the following result of Elstrodt and Roelcke [8, Corollary 3.4].

(2) If λ is a barrelled monotone AK-space, then also its subspace ℒ(λ), consisting of all sequences in λ with zero-density support, is barrelled.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 1 , January 1994 , pp. 57 - 69
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

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