Rosenthal operator spaces

• Autorzy: M. Junge , N. J. Nielsen , T. Oikhberg
• 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.

Kategorie tematyczne

• 46L52: Noncommutative function spaces
• 46L07: Operator spaces and completely bounded maps
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 188
• Numer: 1
• Strony: 17-55

Daty

wydano

2008

Twórcy

autor

M. Junge

• Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, U.S.A.

autor

N. J. Nielsen

• Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

autor

T. Oikhberg

• Department of Mathematics, University of California, Irvine, 103 MSTB, Irvine, CA 92697-3875, U.S.A.

Identyfikatory

DOI

10.4064/sm188-1-2