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Isomorphic Schauder decompositions in certain Banach spaces

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Marchenko V.

Open Mathematics

2014

tom 12

nr 11

1714-1732

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.

Ograniczanie wyników

1 Open Mathematics

1 Marchenko V.

1 2014

Wyniki wyszukiwania

Isomorphic Schauder decompositions in certain Banach spaces