2013/09/25 by Vitalii Marchenko, Marchenko, Vitalii
Mathematics · #46B15 #47A46 #47B40 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46B15 #msc:47A46 #msc:47B40
paper · pdf · doi:10.48550/arxiv.1309.6552
35 pages
arxiv created 2013/09/25 · openalex publication_date 2013/09/25 · arxiv updated 2013/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.