Martín Argerami

On Tate's trace

The problem of whether Tates trace is linear or not is reduced to a special case.

Injective Envelopes and Local Multiplier Algebras of Some Spatial Continuous Trace C -algebras

A precise description of the injective envelope of a spatial con- tinuous trace C � -algebra A over a Stonean spaceis given. The description is based on the notion of a weakly continuous Hilbert bun- dle, which we show herein to be a Kaplansky-Hilbert module over the abelian AW � -algebra C(�). We then use the description of the injective envelope of A to study the first- and second-order local multi- plier algebras of A. In particular, we show that the second-order local multiplier algebra of A is precisely the injective envelope of A.

The Weyl group and the normalizer of a conditional expectation

We define a discrete groupW(E) associated to a faithful normal conditional expectationE : M → N forN ⊑M von Neuman algebras. This group shows the relation between the unitary groupUN and the normalizerNE ofE, which can be also considered as the isotropy of the action of the unitary groupUM ofM onE. It is shown thatW(E) is finite if dimZ(N)<∞ and bounded by the index in the factor case. Also sharp bounds of the order ofW(E) are founded.W(E) appears as the fibre of a covering space defined on the orbit ofE by the natural action of the unitary group ofM. W(E) is computed in some basic examples.

Schur-Horn theorems in II

We describe majorization between selfadjoint operators in a

_\infty

\sigma

-factors

-finite II

A Schur-Horn theorem in II

_\infty

_1

factor

factors

(\mathcal{M},\tau)

Towards the carpenter’s theorem

in terms of simple spectral relations. For a diffuse abelian von Neumann subalgebra