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Unconditionality, Fourier multipliers and Schur multipliers

Cédric Arhancet (2012)

Colloquium Mathematicae

Let G be an infinite locally compact abelian group and X be a Banach space. We show that if every bounded Fourier multiplier T on L²(G) has the property that $T \otimes I d_{X}$ is bounded on L²(G,X) then X is isomorphic to a Hilbert space. Moreover, we prove that if 1 < p < ∞, p ≠ 2, then there exists a bounded Fourier multiplier on $L^{p} (G)$ which is not completely bounded. Finally, we examine unconditionality from the point of view of Schur multipliers. More precisely, we give several necessary and sufficient conditions...

Une relation de chaîne pour les dérivées de Radon-Nikodym spatiales

Jean-Luc Sauvageot (1986)

Bulletin de la Société Mathématique de France

Une remarque sur l'inégalité de Hölder non-commutative

Yao-Zhong Hu (1992)

Séminaire de probabilités de Strasbourg

Unitarily invariant norms related to semi-finite factors

Junsheng Fang, Don Hadwin (2015)

Studia Mathematica

Let ℳ be a semi-finite factor and let 𝓙(ℳ ) be the set of operators T in ℳ such that T = ETE for some finite projection E. We obtain a representation theorem for unitarily invariant norms on 𝓙(ℳ ) in terms of Ky Fan norms. As an application, we prove that the class of unitarily invariant norms on 𝓙(ℳ ) coincides with the class of symmetric gauge norms on a classical abelian algebra, which generalizes von Neumann's classical 1940 result on unitarily invariant norms on Mₙ(ℂ). As another application,...