Displaying similar documents to “Finite-dimensional Schauder decompositions in certain Frechet spaces”

Isomorphic Schauder decompositions in certain Banach spaces

Vitalii Marchenko (2014)

Open Mathematics

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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 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...