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STABILITY OF UNCONDITIONAL SCHAUDER DECOMPOSITIONS IN $\ell _{p}$ SPACES

Part of: General theory of linear operators Special classes of linear operators Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  03 August 2015

VITALII MARCHENKO
VITALII MARCHENKO*
Affiliation:
Mathematical Division, Institute for Low Temperature Physics and Engineering of NAS of Ukraine, 47, Lenin Ave, 61103, Kharkiv, Ukraine email v.marchenko@ilt.kharkov.ua
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Abstract

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We use the best constants in the Khintchine inequality to generalise a theorem of Kato [‘Similarity for sequences of projections’, Bull. Amer. Math. Soc.73(6) (1967), 904–905] on similarity for sequences of projections in Hilbert spaces to the case of unconditional Schauder decompositions in $\ell _{p}$ spaces. We also sharpen a stability theorem of Vizitei [‘On the stability of bases of subspaces in a Banach space’, in: Studies on Algebra and Mathematical Analysis, Moldova Academy of Sciences (Kartja Moldovenjaska, Chişinău, 1965), 32–44; (in Russian)] in the case of unconditional Schauder decompositions in any Banach space.

Keywords

Khintchine inequalityunconditional Schauder decompositionprojectiontypecotypeinfratypeisomorphismSchauder–Orlicz decompositionsymmetric basis

MSC classification

Primary: 46B15: Summability and bases
Secondary: 47A46: Chains (nests) of projections or of invariant subspaces, integrals along chains, etc. 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 444 - 456
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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