The classification problem for von Neumann factors

The classification problem for von Neumann factors

We prove that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 ≤ λ ≤ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type II1 factors is not smooth. We also prove that the isomorphism relation for von Neumann II1 factors is analytic, but is not Borel.

On the Von Neumann Economic Growth Problem

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

The hochschild cohomology problem for von neumann algebras.

In 1967, when Kadison and Ringrose began the development of continuous cohomology theory for operator algebras, they conjectured that the cohomology groups Hn(M, M), n >/= 1, for a von Neumann algebra M, should all be zero. This conjecture, which has important structural implications for von Neumann algebras, has been solved affirmatively in the type I, IIinfinity, and III cases, leaving open o...

The Pukánszky Invariant for Masas in Group Von Neumann Factors

The Pukánszky invariant associates to each maximal abelian self–adjoint subalgebra (masa) A in a type II1 factor M a certain subset ot N ∪ {∞}, denoted Puk(A). We study this invariant in the context of factors generated by infinite conjugacy class discrete countable groups G with masas arising from abelian subgroups H. Our main result is that we are able to describe Puk(V N(H)) in terms of the ...