Non commutative Khintchine and Paley inequalities
Let \(E\) be a symmetric sequence space and let \(C_ E\) be the Schatten space of compact operators on a separable Hilbert space associated with \(E\). For the case \(E=\ell_ 1\) and for the more general case of 2- concave \(E\)'s a non-commutative analogue of Khinchin's inequality is proved. This analogue has been obtained as a consequence of the description of the space \(H^ 1_ \Lambda(C_ E)\), the range space of the projection \(P\otimes Id: H^ 1(C_ E)\to H^ 1(C_ E)\), where \(P: H^ 1(T)\to H^ 1_ \Lambda(T)\) (\(\Lambda=\{2^ n\mid\;n\geq 0\}\)) is the Paley projection. Boundedness of \(P\otimes Id: H^ 1(X)\to H^ 1(X)\) is also studied when \(X=Y\hat\otimes Z\) is the projective tensor product of Banach spaces satisfying some suitable assumptions.
Schatten space of compact operators on a separable Hilbert space
non-commutative analogue of Khinchin's inequality
projective tensor product of Banach spaces
scientific article; zbMATH DE number 60551
scientific article