Domination of operators in the non-commutative setting

• Autorzy: Timur Oikhberg , Eugeniu Spinu
• Języki publikacji: EN

Abstrakty

EN

We consider majorization problems in the non-commutative setting. More specifically, suppose E and F are ordered normed spaces (not necessarily lattices), and 0 ≤ T ≤ S in B(E,F). If S belongs to a certain ideal (for instance, the ideal of compact or Dunford-Pettis operators), does it follow that T belongs to that ideal as well? We concentrate on the case when E and F are C*-algebras, preduals of von Neumann algebras, or non-commutative function spaces. In particular, we show that, for C*-algebras 𝓐 and ℬ, the following are equivalent: (1) at least one of the two conditions holds: (i) 𝓐 is scattered, (ii) ℬ is compact; (2) if 0 ≤ T ≤ S : 𝓐 → ℬ, and S is compact, then T is compact.

Kategorie tematyczne

• 46L52: Noncommutative function spaces
• 46L05: General theory of C * -algebras
• 47L20: Operator ideals
• 47B60: Operators on ordered spaces
• 46B42: Banach lattices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 219
• Numer: 1
• Strony: 35-67

Daty

wydano

2013

Twórcy

autor

Timur Oikhberg

• Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.

autor

Eugeniu Spinu

• Department of Mathematical and, Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada

Identyfikatory

DOI

10.4064/sm219-1-3