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Results tagged with oa.operator-algebras
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user 36687
Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry
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An additive formula for the join of two projection operators
Since every $x \in \mathcal H$ can be deocmposed into a component in $\text{ran}(P \vee Q)$ and a component in $\text{ran}(P \vee Q)^\perp$, it is enough to show that the operator equality holds only …
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An additive formula for the join of two projection operators
Consider the projection lattice of $\mathcal B(\mathcal H)$, the algebra of bounded operators on a Hilbert space $\mathcal H$. In particular, for two (orthogonal) projections $P, Q \in \mathcal B(\mat …
- 1,731
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1
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A relation among projections of a von Neumann algebra
This is a follow-up question on this. Let $A$ be a von Neumann algebra and $P$ be its projection lattice.
For $p,s,q \in P$, let us define $ p \perp q \mid s \iff ps^\perp q = 0$ where $s^\perp = 1- …
- 1,731
2
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139
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A congruence relation on the projection lattice
This question is a continuation of what I asked here. Tristan Bice showed the following nice result there:
Let $A$ be a von Neumann algebra and $P$ its projection lattice, ordered by $p\leq q\Leftrig …
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