PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Studia Mathematica

2008 | 188 | 1 | 17-55
Tytuł artykułu

### Rosenthal operator spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In 1969 Lindenstrauss and Rosenthal showed that if a Banach space is isomorphic to a complemented subspace of an $L_{p}$-space, then it is either an $L_{p}$-space or isomorphic to a Hilbert space. This is the motivation of this paper where we study non-Hilbertian complemented operator subspaces of non-commutative $L_{p}$-spaces and show that this class is much richer than in the commutative case. We investigate the local properties of some new classes of operator spaces for every 2 < p < ∞ which can be considered as operator space analogues of the Rosenthal sequence spaces from Banach space theory, constructed in 1970. Under the usual conditions on the defining sequence σ we prove that most of these spaces are operator $L_{p}$-spaces, not completely isomorphic to previously known such spaces. However, it turns out that some column and row versions of our spaces are not operator $L_{p}$-spaces and have a rather complicated local structure which implies that the Lindenstrauss-Rosenthal alternative does not carry over to the non-commutative case.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
17-55
Opis fizyczny
Daty
wydano
2008
Twórcy
autor
• Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, U.S.A.
autor
• Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
autor
• Department of Mathematics, University of California, Irvine, 103 MSTB, Irvine, CA 92697-3875, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory