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Singularities of embedding operators between symmetric function spaces on [0, 1]

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Abstract

The properties of the identity embedding operatorI(X 1,X 2) (X 1 ⊂X 2) between symmetric function spaces on [0, 1] such as weak compactness, strict singularity (in two versions), and the property of being absolutely summing are examined. Banach and quasi-Banach spaces are considered. A complete description of the linear hull closed with respect to measure of a sequence (g (r) n ) of independent symmetric equidistributed random variables with

$$d(g_n^{(r)} ;t) = meas(\omega :|g_n^{(r)} (\omega )| > t) = \frac{1}{{t^r }} for t \geqslant 1 and 0< r< \infty $$

is obtained, and the boundaries for this space on the scale of symmetric spaces are found.

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Authors and Affiliations

  1. Samara State University, Russia

    S. Ya. Novikov

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  1. S. Ya. Novikov
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Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 549–563, October, 1997.

Translatled by O. V. Sipacheva

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Novikov, S.Y. Singularities of embedding operators between symmetric function spaces on [0, 1]. Math Notes 62, 457–468 (1997). https://doi.org/10.1007/BF02358979

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  • DOI: https://doi.org/10.1007/BF02358979

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