Unconditionality, Fourier multipliers and Schur multipliers

• Autorzy: Cédric Arhancet
• Języki publikacji: EN

Abstrakty

EN

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 $T ⊗ Id_X$ 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 for an operator space to be completely isomorphic to an operator Hilbert space.

Kategorie tematyczne

• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 46L07: Operator spaces and completely bounded maps
• 46L51: Noncommutative measure and integration
• 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 127
• Numer: 1
• Strony: 17-37

Daty

wydano

2012

Twórcy

autor

Cédric Arhancet

• Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France

Identyfikatory

DOI

10.4064/cm127-1-2