We use the concept of a regular object with respect to another object in an arbitrary category, defined in [3], in order to obtain the transfer of regularity in the sense of Zelmanowitz between the categories R−mod and S−mod, when S is an excellent extension of the ring R. Consequently, we obtain a result of [5]: if S is an excellent extension of the ring R, then S is von Neumann regular ring i...

We prove Khintchine type inequalities for words of a fixed length in a reduced free product of C∗-algebras (or von Neumann algebras). These inequalities imply that the natural projection from a reduced free product onto the subspace generated by the words of a fixed length d is completely bounded with norm depending linearly on d. We then apply these results to various approximation properties ...

There is a Banach algebra satisfying the von Neumann inequality for polynomials in a single variable, without constant term, which is not isomorphic to a norm-closed algebra of operators on a Hilbert space.

Normal conditional expectations E : M → N ⊆ M of finite index on von Neumann algebras M with discrete center are investigated to find an estimate for the minimal number of generators of M as a Hilbert N -module. Analyzing the case of M being finite type I with discrete center we obtain that these von Neumann algebras M are always finitely generated projective N -modules with a minimal generator...

We introduce “embedding dimensions” of a family of generators of a finite von Neumann algebra when the von Neumann algebra can be faithfully embedded into the ultrapower of the hyperfinite II1 factor. These embedding dimensions are von Neumann algebra invariants, i.e., do not depend on the choices of the generators. We also find values of these invariants for some specific von Neumann algebras.

We prove that a finite von Neumann algebra A is semisimple if the algebra of affiliated operators U of A is semisimple. When A is not semisimple, we give the upper and lower bounds for the global dimensions of A and U . This last result requires the use of the Continuum Hypothesis.

We prove that every 2-local derivation from the algebra Mn(A)(n > 2) into its bimodule Mn(M) is a derivation, where A is a unital Banach algebra and M is a unital A-bimodule such that each Jordan derivation from A into M is an inner derivation, and that every 2-local derivation on a C*-algebra with a faithful traceable representation is a derivation. We also characterize local and 2-local Lie d...

Suppose F is a finite set of selfadjoint elements in a tracial von Neumann algebra M . For α > 0, F is α-bounded if Pα(F ) < ∞ where Pα is the α-packing entropy of F introduced in [7]. We say that M is strongly 1-bounded if M has a 1-bounded finite set of selfadjoint generators F such that there exists an x ∈ F with χ(x) > −∞. It is shown that if M is strongly 1-bounded, then any finite set of ...

For a finite group scheme G, we continue our investigation of those finite dimensional kG-modules which are of constant Jordan type. We introduce a Quillen exact category structure C(kG) on these modules and investigate K0(C(kG)). We study which Jordan types can be realized as the Jordan types of (virtual) modules of constant Jordan type. We also briefly consider thickenings of C(kG) inside the...

A self-adjoint element in a finite AW*-factor is spectrally symmetric, if its spectral measure under the quasitrace is invariant under the change of variables t 7−→ −t. We show that if A is an AW*-factor of type II1, a self-djoint element in A, without full support, has quasitrace zero, if and only if it can be written as a sum of at most three commuting spectrally symmetric elements. Introduct...