Rosenthal operator spaces (original) (raw)

Unconditional basic sequences and homogeneous Hilbertian subspaces of non-commutative LpL_pLp spaces

Indiana University Mathematics Journal, 2007

Suppose A is a von Neumann algebra with a normal faithful normalized trace τ. We prove that if E is a homogeneous Hilbertian subspace of L p (τ) (1 ≤ p < ∞) such that the norms induced on E by L p (τ) and L 2 (τ) are equivalent, then E is completely isomorphic to the subspace of L p ([0, 1]) spanned by Rademacher functions. Consequently, any homogeneous subspace of L p (τ) is completely isomorphic to the span of Rademacher functions in L p ([0, 1]). In particular, this applies to the linear span of operators satisfying the canonical anti-commutation relations. We also show that the real interpolation space (R, C) θ,p embeds completely isomorphically into L p (R) (R is the hyperfinite II 1 factor) for any 1 ≤ p < 2 and θ ∈ (0, 1).

More Properties of the Classes of Hereditarilyp Banach Sequence Spaces

2011

Hagler and Azimi have introduced a class of hereditarily � 1 Banach spaces (Xα,p) which fails the Schur property (3) and in 2002, Azimi generalized this spaces to Xα,p (1 <p< ∞) as hereditarilyp Banach spaces (1). We show that Xα,1 has not the anti-Daugavet property for compact operators and for operators of rank 1. Also, the Banach spaces Xα,p fail the DP ∗ -property. Some other properties of this spaces are studied.

On some new sequence spaces of non-absolute type related to the spaces ℓp and ℓ∞ I

Filomat, 2011

In the present paper, which is a natural continuation of the work done in [13], we determine the α-, β-and γ-duals of the sequence spaces λ p and λ ∞ of non-absolute type, where 1 ≤ p < ∞. Further, we characterize some related matrix classes and deduce the characterizations of some other classes by means of a given basic lemma.

A Class of Hereditarily ℓ p (c 0 ) Banach Spaces

We extend the class of Banach sequence spaces constructed by Ledari, as presented in "A class of hereditarily ℓ1 Ba-nach spaces without Schur property" and obtain a new class of hereditarily ℓp(c0) Banach spaces for 1 ≤ p < ∞. Some other properties of this spaces are studied.

spaces—the local structure of non-commutative Lp spaces

Advances in Mathematics, 2004

Developing the theory of COL p spaces (a variation of the non-commutative analogue of L p spaces), we provide new tools to investigate the local structure of non-commutative L p spaces. Under mild assumptions on the underlying von Neumann algebras, non-commutative L p spaces with Grothendieck's approximation property behave locally like the space of matrices equipped with the p-norm (of the sequences of their singular values). As applications, we obtain a basis for non-commutative L p spaces associated with hyperfinite von Neumann algebras with separable predual von Neumann algebras generated by free groups, and obtain a basis for separable nuclear C Ã -algebras. r

COL p spaces¿the local structure of non-commutative L p spaces

Advances in Mathematics, 2004

Developing the theory of COL p spaces (a variation of the non-commutative analogue of L p spaces), we provide new tools to investigate the local structure of non-commutative L p spaces. Under mild assumptions on the underlying von Neumann algebras, non-commutative L p spaces with Grothendieck's approximation property behave locally like the space of matrices equipped with the p-norm (of the sequences of their singular values). As applications, we obtain a basis for non-commutative L p spaces associated with hyperfinite von Neumann algebras with separable predual von Neumann algebras generated by free groups, and obtain a basis for separable nuclear C Ã -algebras. r

On some properties of new paranormed sequence space of non-absolute type

2011

In this work, we introduce some new generalized sequence space related to the space l(p). Furthermore we investigate some topological properties as the completeness, the isomorphism and also we give some inclusion relations between this sequence space and some of the other sequence spaces. In addition, we compute alpha-, beta- and gamma-duals of this space, and characterize certain matrix transformations on this sequence space.