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Register a new userIsomorphic Schauder decompositions in certain Banach spaces
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Authors
Vitalii Marchenko
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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 $ell_{Psi}$-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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