Multi-indexed p-orthogonal sums in non-commutative Lebesgue spaces

DOI10.1512/IUMJ.2004.53.2576zbMATH Open1065.46044arXivmath/0312275OpenAlexW1993778557MaRDI QIDQ4831965

Javier Parcet

Publication date: 3 January 2005

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Abstract: In this paper we extend a recent Pisier's inequality for p-orthogonal sums in non-commutative Lebesgue spaces. To that purpose, we generalize the notion of p-orthogonality to the class of multi-indexed families of operators. This kind of families appear naturally in certain non-commutative Khintchine type inequalities associated with free groups. Other p-orthogonal families are given by the homogeneous operator-valued polynomials in the Rademacher variables or the multi-indexed martingale difference sequences. As in Pisier's result, our tools are mainly combinatorial.

Full work available at URL: https://arxiv.org/abs/math/0312275

zbMATH Keywords

finite von Neumann algebra\(p\)-orthogonal familiesinequalities for multi-indexed families

Mathematics Subject Classification ID

Noncommutative measure and integration (46L51) Noncommutative function spaces (46L52)

Related Items (1)

An inequality for \(p\)-orthogonal sums in non-commutative \(L_p\)

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