Diagonalizing Matrices over Aw*-algebras
نویسندگان
چکیده
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*-
منابع مشابه
On nest modules of matrices over division rings
Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...
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...
متن کاملActive 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 کاملOn p-semilinear transformations
In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...
متن کامل