Isomorphic Schauder decompositions in certain Banach spaces

Vitalii Marchenko

Open Mathematics, Tome 12 (2014), p. 1714-1732 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2014-01-01

Zbl 1308.47011

EUDML-ID : urn:eudml:doc:269687

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