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Isomorphic Schauder decompositions in certain Banach spaces

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Central European Journal of Mathematics

Abstract

We extend a theorem of Kato on similarity for sequences of projections in Hilbert spaces to the case of isomorphic Schauder decompositions in certain Banach spaces. To this end we use ℓψ-Hilbertian and ∞-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition to the case of Banach spaces and introduce the class of Banach spaces with Schauder-Orlicz decompositions. Furthermore, we generalize the notions of type, cotype, infratype and M-cotype of a Banach space and study the properties of unconditional Schauder decompositions in Banach spaces possessing certain geometric structure.

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  1. Department of Mathematics and Mechanics, V.N. Karazin Kharkiv National University, Svobody Sq. 4, 61022, Kharkiv, Ukraine

    Vitalii Marchenko

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  1. Vitalii Marchenko
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Marchenko, V. Isomorphic Schauder decompositions in certain Banach spaces. centr.eur.j.math. 12, 1714–1732 (2014). https://doi.org/10.2478/s11533-014-0441-y

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