Journal article
Coordinates for triangular operator algebras. II
Pacific journal of mathematics, Vol.137(2), pp.335-369
1989
DOI: 10.2140/pjm.1989.137.335
Abstract
Let M be a von Neumann algebra and let A be a maximal abelian self-adjoint subalgebra (masa) of M. A subalgebra T of M is called triangular (with respect to A) if T {n-ary intersection} T* = A, where T* denotes the collection of adjoints of the elements in T. If T is not contained in any larger triangular subalgebra of M, then T is called maximal triangular. If A is a Cartan subalgebra, then M may be realized as an algebra of matrices indexed by an equivalence relation on a standard Borel space and if T is σ-weakly closed and maximal triangular, then T may be realized as the collection of matrices supported on the graph of a partial order that totally orders each equivalence class. In this paper we will be concerned with the relation between the structure of these algebras and the theory of analytic operator algebras. It turns out that this relation is complex: it involves the cohomology of the equivalence relation, the order type of the partial order and the type of M. © 1989 by Pacific Journal of Mathematics.
Details
- Title: Subtitle
- Coordinates for triangular operator algebras. II
- Creators
- Paul MuhlyKichi-Suke SaitoBaruch Solel
- Resource Type
- Journal article
- Publication Details
- Pacific journal of mathematics, Vol.137(2), pp.335-369
- DOI
- 10.2140/pjm.1989.137.335
- ISSN
- 0030-8730
- eISSN
- 1945-5844
- Language
- English
- Date published
- 1989
- Academic Unit
- Statistics and Actuarial Science; Mathematics
- Record Identifier
- 9984397202102771
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