We prove that every positive trace on a countably generated ∗-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial ∗-algebra can be embedded into a metric ultraproduct of generic matrix algebras. As a particular consequence, every finite von Neumann algebra with separable pre-dual can be embedded into an ultraproduct...

Throughout this paper A will denote a finite-dimensional associative complex algebra. A vector space norm · on A is said to be stable if there exists a positive constant σ satisfying x ≤ σ x n for every x in A and all natural numbers n. It is well known that stable norms · on A are spectrally dominant (that is, for every x in A, the inequality ρ x ≤ x holds, where ρ · denotes the spectral radiu...

In the first part of this article we prove that one conditions required in original definition nearly Frobenius algebra, coassociativity, is redundant. Also, determine dimension product and tensor two algebras from each them. We apply these results to semisimple algebras. second introduce notion normalized algebra. a series equivalences: concept algebra equivalent separable fact projective as b...

We show that an excellent local domain of characteristic p has a separable big Cohen–Macaulay algebra. In the course of our work we prove that an element which is in the Frobenius closure of an ideal can be forced into the expansion of the ideal to a module-finite separable extension ring.

If a nuclear separable C*-algebra A can be approximated by C*-subalgebras satisfying the UCT, then A satisfies the UCT. It is also shown that the validity of the UCT for all separable nuclear C*-algebras is equivalent to a certain finite dimensional approximation property.

Let A and B be separable nuclear continuous C(X)-algebras over a finite dimensional compact metrizable space X. It is shown that an element σ of the parametrized Kasparov group KKX(A,B) is invertible if and only all its fiberwise components σx ∈ KK(A(x), B(x)) are invertible. This criterion does not extend to infinite dimensional spaces since there exist nontrivial unital separable continuous f...

Using Paschke-Higson Duality [Hig][Pa], we get a natural index pairingKi(A)×Ki+1(DΦ) → Z where i = 0, 1(mod2) and A is a separable C ∗ -algebra, Φ is a representation of A on a separable Hilbert space H. We prove this is a special case of Kasparov Product [Kas].

Abstract We prove a double commutant theorem for separable subalgebras of wide class corona C * -algebras, largely resolving problem posed by Pedersen in 1988. Double theorems originated with von Neumann, whose seminal result evolved into an entire field now called Neumann algebra theory. Voiculescu later proved -algebraic the Calkin algebra. similar much more general so-called -algebras.