Complemented subspaces of symmetric function spaces

Tokarev, Eugene

doi:10.1007/bf01152379

Cited by 4 publications

(1 citation statement)

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“…If a separable symmetric space X does not contain 2 as a complementary sublattice, then the condition G ⊂ X ⊂ G is necessary and sufficient for X to contain 2 as a complementary subspace. Similar (but not so general) results were obtained by Tokarev in [136].…”

Section: This Implies the Inequalitysupporting

confidence: 86%

Rademacher functions in symmetric spaces

Асташкин

2010

J Math Sci

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The Rademacher system or the Bernoulli sequence of independent, identically and symmetrically distributed random variables taking values ±1 is a classical object of orthogonal series theory and probability theory. It has many applications in other fields as well, first of all, in the geometric theory of Banach spaces, theory of operators, harmonic analysis, and mathematical statistics. The topic of this monograph is more specific: the study of the Rademacher system in symmetric (rearrangement invariant) functional spaces. The first work devoted to this problem (apart from the classical results for L p -spaces such as the Khintchine inequality) is an article by Rodin and Semenov that was published in 1975. A number of principal problems related to the behavior of Rademacher systems in symmetric spaces was posed and the path for further investigations was indicated. We recall that the initial works on general symmetric spaces (first of all, works of G. Lorentz and Semenov) appeared in 50s-60s of the last century. Then [92,96,97] summarized a certain stage of the investigations.Investigations of the Rademacher systems in symmetric spaces received renewed impetus in 90th after the works by S. Montgomery-Smith and P. Hitchenko, where they refined the Khintchine inequality. The main role was played by the Peetre K-functional.

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Section: This Implies the Inequalitysupporting

confidence: 86%