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Subtag of the [oa.operator-algebras] tag for questions about von Neumann algebras, that is, weak operator topology closed, unital, *-subalgebras of bounded operators on a Hilbert space.

4 votes
2 answers
386 views

v-Na generated by

Given two free semicirculars X_1 and X_2 and a projection h in the von-Neumann algebra generated by X_1, how does one show that the von-Neumann algebra generated by {X_1, hX_2(1-h)} is a factor? It is …
Madhushree's user avatar
0 votes
0 answers
152 views

For a separable v-N algebra M, how to see $M \rtimes \mathbb{R}$ as a subalgebra of $M \otim...

For a v-N algebra $M$ acting as bounded operators on a separable Hilbert space $H$, how to see $M \rtimes \mathbb{R}$ as a subalgebra of $M \otimes B(L^2(\mathbb{R})$? Why I am confused is because $ …
Madhushree's user avatar
2 votes
1 answer
238 views

when is an element of $M_n(M)$ $\ast$-free from $M_n(\mathbb{C})$ for a $\ast$-non-commutati...

From "Lectures on the combinatorics of free probability" by Nica and Speicher we have a necessary sufficient criteria for an element of $M_n(M)$ being free from $M_n(\mathbb{C})$ for a non-commutative …
Madhushree's user avatar