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Speaker: Fedor Sukochev, U. New South Wales
Title: Invariant subspaces and upper triangular forms for classes of infinite dimensional operators
Abstract: In classical matrix theory, a matrix can be written in upper triangular form with help of its invariant subspaces. A similar result, due to Ringrose in 1962, holds for compact operators on infinite dimensional Hilbert space. Using recent results of Haagerup and Schultz, we prove an analogous result for certain non-compact operators on Hilbert space, namely, for those in finite von Neumann algebras. The talk may also include some new results concerning triangular form of unbounded operators affiliated with finite von Neumann algebras and some speculation about invariant subspace problems for elements of finite von Neumann algebras.(Joint work with Ken Dykema and Dmitriy Zanin).
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