TY - JOUR

T1 - On tensor products of nuclear operators in Banach spaces

AU - Reinov, Oleg

PY - 2021/12/22

Y1 - 2021/12/22

N2 - 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.

AB - 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.

U2 - 10.15673/tmgc.v14i3.2083

DO - 10.15673/tmgc.v14i3.2083

M3 - Article

VL - 14

SP - 187

EP - 205

JO - Proceedings of the International Geometry Center

JF - Proceedings of the International Geometry Center

SN - 2072-9812

IS - 3

ER -