We give a characterization of all the unitarily invariant norms on finite von Neumann algebra acting separable Hilbert space. The is analogous to Neumann’s for $$n\times n$$ complex matrices and in Fang et al. (J Funct Anal 255(1):142–183, 2008) $$II_{1}$$ factors.

and Applied Analysis 3 Lemma 2.2 see 5, Theorem 3.3 , 6, Theorem 3.3 . Let A be a simple unital C∗-algebra. If TRR A 0, then RR A 0. If Tsr A 1 and has the (SP)-property, then tsr A 1. Definition 2.3 see 13, Definition 1.2 . Let A be an infinite dimensional finite simple separable unital C∗-algebra, and let α : G → Aut A be an action of a finite group G on A. We say that α has the tracial Rokhl...

We apply to operator algebra theory a monotone selection principle which apparently escaped attention (of operator algebra theorists) so far. This principle relates to the basic order theoretic characterisation of von Neumann algebras given by Kadison, and the simplified form this result takes in separable Hilbert spaces. In the separable case we need only consider increasing sequences rather t...

We present a unified approach to the study of separable and Frobenius algebras. The crucial observation is that both types of algebras are related to the nonlinear equation RR = RR = RR, called the FS-equation. Given a solution to the FS-equation satisfying a certain normalizing condition, we can construct a Frobenius algebra or a separable algebra A(R) the normalizing condition is different in...

An efficient direct parallel elliptic solver based on the spectral element discretization is developed. The direct solver is based on a matrix decomposition approach which reduces multi-dimensional separable problems to a sequence of onedimensional problems that can be efficiently handled by a static condensation process. Thanks to the spectral accuracy and the localized nature of a spectral el...

Let A be a separable C∗-algebra and let B be a stable C∗-algebra with a strictly positive element. We consider the (semi)group Ext(A,B) (resp. Ext(A,B)) of homotopy classes of asymptotic (resp. of genuine) homomorphisms from A to the corona algebra M(B)/B and the natural map i : Ext(A,B) −→ Ext(A,B). We show that if A is a suspension then Ext(A,B) coincides with E-theory of Connes and Higson an...

We will demonstrate that ifM is an uncountable compact metric space, then there is an action of the Polish group of all continuous functions from M to U(1) on a separable probability algebra which preserves the measure and yet does not admit a point realization in the sense of Mackey. This is achieved by exhibiting a strong form of ergodicity of the Boolean action known as whirliness. This is i...

Let A be a simple, separable C∗-algebra of stable rank one. We prove that the Cuntz semigroup of C(T, A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yield...

Let A be a separable exact quasidiagonal C*-algebra. Suppose that ?: A L(H) is a faithful representation whose image does not contain nonzero compact operators. Then there exists a sequence .n : A L(H) of completely positive contractions such that &?(a)&.n(a)& 0 for all a # A, and the C*-algebra generated by .n(A) is finite dimensional for each n. As an application it is shown that if the C*-al...

In the topology of coordinatewise convergence ∇∞ is a compact, metrizable and separable space. Denote by C(∇∞) the algebra of real continuous functions on ∇∞ with pointwise operations and the supremum norm. In C(∇∞) there is a distinguished dense subspace F := R [q1, q2, . . . ] generated (as a commutative unital algebra) by algebraically independent continuous functions qk(x) := ∑∞ i=1 x k+1 i...