30,092 research outputs found
Algebraic orthogonality and commuting projections in operator algebras
We describe absolutely ordered -normed spaces, for
which presents a model for "non-commutative" vector lattices and includes order
theoretic orthogonality. To demonstrate its relevance, we introduce the notion
of {\it absolute compatibility} among positive elements in absolute order unit
spaces and relate it to symmetrized product in the case of a
C-algebra. In the latter case, whenever one of the elements is a
projection, the elements are absolutely compatible if and only if they commute.
We develop an order theoretic prototype of the results. For this purpose, we
introduce the notion of {\it order projections} and extend the results related
to projections in a unital C-algebra to order projections in an
absolute order unit space. As an application, we describe spectral
decomposition theory for elements of an absolute order unit space.Comment: 2
Why Texas feels less subprime stress than U.S.
Differences in economic factors and mortgage characteristics give the state a lower delinquency rate.Economic conditions - Texas ; Mortgage loans ; Foreclosure ; Subprime mortgage ; Housing - Prices
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