Schauder Decompositions and the Grothendieck and Dunford-Pettis Properties in Köthe Echelon Spaces of Infinite Order

Schauder Decompositions and the Grothendieck and Dunford-Pettis Properties in Köthe Echelon... It is shown that every echelon space λ∞(A), with A an arbitrary Köthe matrix, is a Grothendieck space with the Dunford-Pettis property. Since λ∞(A) is Montel if and only if it coincides with λ0(A), this identifies an extensive class of non-normable, non-Montel Fréchet spaces having these two properties. Even though the canonical unit vectors in λ∞(A) fail to form an unconditional basis whenever λ∞(A) ≠ λ0(A), it is shown, nevertheless, that in this case λ∞(A) still admits unconditional Schauder decompositions (provided it satisfies the density condition). This is in complete contrast to the Banach space setting, where Schauder decompositions never exist. Consequences for spectral measures are also given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Schauder Decompositions and the Grothendieck and Dunford-Pettis Properties in Köthe Echelon Spaces of Infinite Order

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Publisher
Birkhäuser-Verlag
Copyright
Copyright © 2006 by Birkhäuser Verlag, Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-006-2014-1
Publisher site
See Article on Publisher Site

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