Interpolation between non-commutative BMO and non-commutative Lp-spaces

Maps between Non-commutative Spaces

Let J be a graded ideal in a not necessarily commutative graded k-algebra A = A0⊕A1⊕· · · in which dimk Ai <∞ for all i. We show that the map A→ A/J induces a closed immersion i : Projnc A/J → Projnc A between the non-commutative projective spaces with homogeneous coordinate rings A and A/J . We also examine two other kinds of maps between non-commutative spaces. First, a homomorphism φ : A → B...

Integral Non - Commutative Spaces

Integral Non-commutative Spaces

A non-commutative space X is a Grothendieck category ModX. We say X is integral if there is an indecomposable injective X-module EX such that its endomorphism ring is a division ring and every X-module is a subquotient of a direct sum of copies of EX . A noetherian scheme is integral in this sense if and only if it is integral in the usual sense. We show that several classes of non-commutative ...

EMBEDDINGS OF NON - COMMUTATIVE Lp - SPACES INTO NON - COMMUTATIVE L 1 - SPACES , 1 < p < 2 Marius Junge

It will be shown that for 1 < p < 2 the Schatten p-class is isometrically isomorphic to a subspace of the predual of a von Neumann algebra. Similar results hold for non-commutative Lp(N, τ)-spaces defined by a finite trace on a finite von Neumann algebra. The embeddings rely on a suitable notion of p-stable processes in the non-commutative setting. Introduction and Notation The theory of p-stab...

HOMOGENEOUS HILBERTIAN SUBSPACES OF NON-COMMUTATIVE Lp SPACES

December 22, 1999 Abstract. Suppose A is a hyperfinite von Neumann algebra with a normal faithful normalized trace τ . We prove that if E is a homogeneous Hilbertian subspace of Lp(τ) (1 ≤ p < ∞) such that the norms induced on E by Lp(τ) and L2(τ) are equivalent, then E is completely isomorphic to the subspace of Lp([0, 1]) spanned by Rademacher functions. Consequently, any homogeneous Hilberti...