Abelian Strict Approximation in AW*-Algebras and Weyl-von Neumann Type Theorems
| dc.creator | D'Antoni, Claudio | |
| dc.creator | Zsido, Laszlo | |
| dc.date | 2006-06-13 | |
| dc.date.accessioned | 2026-07-07T07:17:14Z | |
| dc.date.available | 2026-07-07T07:17:14Z | |
| dc.description | In this paper, for a C*-Algebra A with M = M(A) an AW*-algebra, or equivalently, for an essential, norm-closed, two-sided ideal A of an AW*-algebra M, we investigate the strict approximability of the elements of M from commutative C*- subalgebras of A. In the relevant case of the norm-closed linear span A of all finite projections in a semi-finite AW*-algebra M we shall give a complete description of the strict closure in M of any maximal abelian self-adjoint subalgebra (masa) of A. We shall see that the situation is completely different for discrete respectively continuous M : in the discrete case, for any masa C of A, the strict closure of C is equal to the relative commutant of C in M, while in the continuous case, under certain conditions concerning the center valued quasitrace of the finite reduced algebras of M (satisfied by all von Neumann algebras), C is already strictly closed. Thus in the continuous case no elements of M which are not already belonging to A can be strictly approximated from commutative C*-subalgebras of A. In spite of this pathology of the strict topology in the case of the norm-closed linear span of all finite projections of a continuous semi-finite AW*-algebra, we shall prove that in general situations including also this case, any normal y in M is equal modulo A to some x in M which belongs to an order theoretical closure of an appropriate commutative C*-subalgebra of A. In other words, if we replace the strict topology with order theoretical approximation, Weyl-von Neumann-Berg-Sikonia type theorems will hold in substantially greater generality. | |
| dc.identifier | https://arxiv.org/abs/math/0606302 | |
| dc.identifier | http://arxiv.org/abs/math/0606302 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113867 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05; 46L10 | |
| dc.title | Abelian Strict Approximation in AW*-Algebras and Weyl-von Neumann Type Theorems | |
| dc.type | text |