Isomorphic Schauder decompositions in certain Banach spaces

• Autorzy: Vitalii Marchenko
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Isomorphic Schauder decompositions; Unconditional Schauder decompositions; Projections; Orlicz spaces

Kategorie tematyczne

• 47A46: Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
• 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.
• 46B15: Summability and bases

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 11
• Strony: 1714-1732

Daty

wydano

2014-11-01

online

2014-06-29

Twórcy

autor

Vitalii Marchenko

• V.N. Karazin Kharkiv National University

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Identyfikatory

DOI

10.2478/s11533-014-0441-y