The quasinormed Neumann–Schatten ideals and embedding theorems for the generalized Lions–Peetre spaces of means

Ovchinnikov, V.

doi:10.1090/S1061-0022-2011-01162-8

The quasinormed Neumann–Schatten ideals and embedding theorems for the generalized Lions–Peetre spaces of means
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by V. I. Ovchinnikov
Translated by: the author

St. Petersburg Math. J. 22 (2011), 669-681

DOI: https://doi.org/10.1090/S1061-0022-2011-01162-8

Published electronically: May 3, 2011

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Abstract:

For the spaces $\varphi (X_0,X_1)_{p_0,p_1}$, which generalize the spaces of means introduced by Lions and Peetre to the case of functional parameters, necessary and sufficient conditions are found for embedding when all parameters (the function $\varphi$ and the numbers $1\leq p_0$, $p_1\leq \infty )$ vary. The proof involves a description of generalized Lions–Peetre spaces in terms of orbits and co-orbits of von Neumann–Schatten ideals (including quasinormed ideals).

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