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Disjointly strictly singular inclusions of symmetric spaces

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Abstract

In this paper, the disjoint strict singularity of inclusions of symmetric spaces of functions on an interval is considered. A condition for the presence of a “gap” between spaces sufficient for the inclusion of one of these spaces into the other to be disjointly strictly singular is found. The condition is stated in terms of fundamental functions of spaces and is exact in a certain sense. In parallel, necessary and sufficient conditions for an inclusion of Lorentz spaces to be disjointly strictly singular (and similar conditions for Marcinkiewicz spaces) are obtained and certain other assertions are proved.

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Authors and Affiliations

  1. Samara State University, USSR

    S. V. Astashkin

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  1. S. V. Astashkin
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Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 3–14, January, 1999.

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Astashkin, S.V. Disjointly strictly singular inclusions of symmetric spaces. Math Notes 65, 3–12 (1999). https://doi.org/10.1007/BF02675003

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