Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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).
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
9-27
Opis fizyczny
Daty
wydano
2002
Twórcy
- Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-2