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s-numbers of projections in Banach spaces


Mascioni, V (1989). s-numbers of projections in Banach spaces. Israel Journal of Mathematics, 67(1):82-94.

Abstract

Given ans-number sequences te {h, x, y, c, d, a, Γ}, we find a characterization of the following property of a Banach spaceX:(P s). There is a constantC>0 such that, for anyn-dimensional subspaceE ofX, we can find a projectionP fromX ontoE with sup k ks k(P)≦Cn. As an application, we prove thatX has weak type 2 if and only ifX is finite dimensionally norming, thus answering a question of Casazza and Shura. Weak Hilbert spaces are also characterized in a new way, the main tool in the proof being a characterization of weak cotype 2 by means of projections. The latter is applied to the study of U.A.P., too.

Given ans-number sequences te {h, x, y, c, d, a, Γ}, we find a characterization of the following property of a Banach spaceX:(P s). There is a constantC>0 such that, for anyn-dimensional subspaceE ofX, we can find a projectionP fromX ontoE with sup k ks k(P)≦Cn. As an application, we prove thatX has weak type 2 if and only ifX is finite dimensionally norming, thus answering a question of Casazza and Shura. Weak Hilbert spaces are also characterized in a new way, the main tool in the proof being a characterization of weak cotype 2 by means of projections. The latter is applied to the study of U.A.P., too.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1989
Deposited On:29 Nov 2010 16:29
Last Modified:05 Apr 2016 13:29
Publisher:Hebrew University Magnes Press
ISSN:0021-2172
Publisher DOI:https://doi.org/10.1007/BF02764901
Related URLs:http://www.ma.huji.ac.il/~ijmath/ (Publisher)

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