Banach Algebras with Involution.
Banach manifolds of algebraic elements in the algebra (H) of bounded linear operatorsof bounded linear operators
Given a complex Hilbert space H, we study the manifold of algebraic elements in . We represent as a disjoint union of closed connected subsets M of Z each of which is an orbit under the action of G, the group of all C*-algebra automorphisms of Z. Those orbits M consisting of hermitian algebraic elements with a fixed finite rank r, (0< r<∞) are real-analytic direct submanifolds of Z. Using the C*-algebra structure of Z, a Banach-manifold structure and a G-invariant torsionfree affine...
Banach principle in the space of τ-measurable operators
We establish a non-commutative analog of the classical Banach Principle on the almost everywhere convergence of sequences of measurable functions. The result is stated in terms of quasi-uniform (or almost uniform) convergence of sequences of measurable (with respect to a trace) operators affiliated with a semifinite von Neumann algebra. Then we discuss possible applications of this result.
Banach-power-associative algebras and J-B algebras
Banach-Saks properties in symmetric spaces of measurable operators
We study Banach-Saks properties in symmetric spaces of measurable operators. A principal result shows that if the symmetric Banach function space E on the positive semiaxis with the Fatou property has the Banach-Saks property then so also does the non-commutative space E(ℳ,τ) of τ-measurable operators affiliated with a given semifinite von Neumann algebra (ℳ,τ).
Banach-Saks properties of C*-algebras and Hilbert C*-modules.
Bergelson's theorem for weakly mixing C*-dynamical systems
We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khinchin's recurrence theorem obtained by Bergelson in the measure-theoretic case. A noncommutative recurrence theorem for such systems is obtained as a corollary.
Bessel and Grüss type inequalities in inner product modules over Banach -algebras.
Best approximation in C*-algebras.
Bibounded operators on W*-algebras.
Bicrossproduct Kac Algebras, Bicrossproduct Groups and von Neumann Algebras of Takesaki's Type.
Bilinear Forms on Exact Operator Spaces and B(H) ? B(H).
Bilipschitz invariance of the first transverse characteristic map
Given a smooth S¹-foliated bundle, A. Connes has shown the existence of an additive morphism ϕ from the K-theory group of the foliation C*-algebra to the scalar field, which factorizes, via the assembly map, the Godbillon-Vey class, which is the first secondary characteristic class, of the classifying space. We prove the invariance of this map under a bilipschitz homeomorphism, extending a previous result for maps of class C¹ by H. Natsume.
Bivariant -theory for locally convex algebras and the Chern-Connes character. (Bivariante -Theorie für lokalconvexe Algebren und der Chern-Connes-Charakter.)
bm-independence and central limit theorems associated with symmetric cones
We present a generalization of the classical central limit theorem to the case of non-commuting random variables which are bm-independent and indexed by a partially ordered set. As the set of indices I we consider discrete lattices in symmetric positive cones, with the order given by the cones. We show that the limit measures have moments which satisfy recurrences generalizing the recurrence for the Catalan numbers.
Bounded elements and spectrum in Banach quasi *-algebras
A normal Banach quasi *-algebra (,) has a distinguished Banach *-algebra consisting of bounded elements of . The latter *-algebra is shown to coincide with the set of elements of having finite spectral radius. If the family () of bounded invariant positive sesquilinear forms on contains sufficiently many elements then the Banach *-algebra of bounded elements can be characterized via a C*-seminorm defined by the elements of ().
Brascamp--Lieb inequalities for non-commutative integration.
Brisure de symétrie spontanée et géométrie du point de vue spectral
Bundle Convergence in a von Neumann Algebra and in a von Neumann Subalgebra
Let H be a separable complex Hilbert space, 𝓐 a von Neumann algebra in 𝓛(H), ϕ a faithful, normal state on 𝓐, and 𝓑 a commutative von Neumann subalgebra of 𝓐. Given a sequence (Xₙ: n ≥ 1) of operators in 𝓑, we examine the relations between bundle convergence in 𝓑 and bundle convergence in 𝓐.