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arXiv · 1309.6552

Isomorphic Schauder decompositions in certain Banach spaces

Vitalii Marchenko
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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 $\ell_Ψ$-Hilbertian and $\infty$-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition in a Hilbert space and introduce the class of 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 spaces possessing certain geometric structure.

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Vitalii Marchenko. 2013-09-25. Isomorphic Schauder decompositions in certain Banach spaces. https://arxiv.org/abs/1309.6552

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