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On asymptotically symmetric Banach spaces

M. JungeD. KutzarovaE. Odell — 2006

Studia Mathematica

A Banach space X is asymptotically symmetric (a.s.) if for some C < ∞, for all m ∈ ℕ, for all bounded sequences ( x j i ) j = 1 X , 1 ≤ i ≤ m, for all permutations σ of 1,...,m and all ultrafilters ₁,...,ₘ on ℕ, l i m n , . . . l i m n , | | i = 1 m x n i i | | C l i m n σ ( 1 ) , σ ( 1 ) . . . l i m n σ ( m ) , σ ( m ) | | i = 1 m x n i i | | . We investigate a.s. Banach spaces and several natural variations. X is weakly a.s. (w.a.s.) if the defining condition holds when restricted to weakly convergent sequences ( x j i ) j = 1 . Moreover, X is w.n.a.s. if we restrict the condition further to normalized weakly null sequences. If X is a.s. then all spreading...

Rosenthal operator spaces

M. JungeN. J. NielsenT. Oikhberg — 2008

Studia Mathematica

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...

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