AW∗-algebras are QW∗-algebras
نویسندگان
چکیده
منابع مشابه
Active Lattices Determine Aw*-algebras
We prove that AW*-algebras are determined by their projections, their symmetries, and the action of the latter on the former. We introduce active lattices, which are formed from these three ingredients. More generally, we prove that the category of AW*-algebras is equivalent to a full subcategory of active lattices. Crucial ingredients are an equivalence between the category of piecewise AW*-al...
متن کاملDiagonalizing Matrices over Aw*-algebras
Every commuting set of normal matrices with entries in an AW*algebra can be simultaneously diagonalized. To establish this, a dimension theory for properly infinite projections in AW*-algebras is developed. As a consequence, passing to matrix rings is a functor on the category of AW*-
متن کاملCategorical Aspects of von Neumann Algebras and AW ∗ - algebras Sander
We take a look at categorical aspects of von Neumann algebras, constructing products, coproducts, and more general limits, and colimits. We shall see that exponentials and coexponentials do not exist, but there is an adjoint to the spatial tensor product, which takes the role of coexponent. We then introduce the class of AW*-algebras and try to see to what extend these categorical constructions...
متن کاملSpectral and Polar Decomposition in AW*-Algebras
The spectral decomposition of normal linear (bounded) operators and the polar decomposition of arbitrary linear (bounded) operators on Hilbert spaces have been interesting and technically useful results in operator theory [3, 9, 13, 20]. The development of the concept of von Neumann algebras on Hilbert spaces has shown that both these decompositions are always possible inside of the appropriate...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1967
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1967.23.97