Open AccessOn tensor products of nuclear operators in Banach spaces
Author(s) -
O. I. Reinov
Publication year - 2021
Publication title -
trudy meždunarodnogo geometričeskogo centra/pracì mìžnarodnogo geometričnogo centru
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.124
H-Index - 2
eISSN - 2409-8906
pISSN - 2072-9812
DOI - 10.15673/tmgc.v14i3.2083
Subject(s) - mathematics , lorentz transformation , hilbert space , pure mathematics , scalar (mathematics) , abelian group , convolution (computer science) , banach space , lorentz space , fourier transform , tensor (intrinsic definition) , operator (biology) , operator theory , chemistry , mathematical analysis , physics , quantum mechanics , computer science , repressor , biochemistry , geometry , machine learning , artificial neural network , transcription factor , gene
The following result of G. Pisier contributed to the appearance of this paper: if a convolution operator ★f : M(G) → C(G), where $G$ is a compact Abelian group, can be factored through a Hilbert space, then f has the absolutely summable set of Fourier coefficients. We give some generalizations of the Pisier's result to the cases of factorizations of operators through the operators from the Lorentz-Schatten classes Sp,q in Hilbert spaces both in scalar and in vector-valued cases. Some applications are given.