Spectral subspaces and non-commutative Hilbert transforms

• Autorzy: Narcisse Randrianantoanina
• Języki publikacji: EN

Abstrakty

EN

Let G be a locally compact abelian group and ℳ be a semifinite von Neumann algebra with a faithful semifinite normal trace τ. We study Hilbert transforms associated with G-flows on ℳ and closed semigroups Σ of Ĝ satisfying the condition Σ ∪ (-Σ) = Ĝ. We prove that Hilbert transforms on such closed semigroups satisfy a weak-type estimate and can be extended as linear maps from L¹(ℳ,τ) into $L^{1,∞}(ℳ, τ)$. As an application, we obtain a Matsaev-type result for p = 1: if x is a quasi-nilpotent compact operator on a Hilbert space and Im(x) belongs to the trace class then the singular values ${μₙ(x)}_{n=1}^{∞}$ of x are O(1/n).

Kategorie tematyczne

• 46L52: Noncommutative function spaces
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)
• 22D25: C * -algebras and W * -algebras in relation to group representations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 91
• Numer: 1
• Strony: 9-27

Daty

wydano

2002

Twórcy

autor

Narcisse Randrianantoanina

• Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, U.S.A.

Identyfikatory

DOI

10.4064/cm91-1-2