UNITARY INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS

Improper Filtrations for C-algebras: Spectra of Unilateral Tridiagonal Operators

Let A ⊆ B(H) be a C∗-algebra of operators and let P1 ≤ P2 ≤ . . . be an increasing sequence of finite dimensional projections in B(H). In a previous paper [3] we developed methods for computing the spectrum of self adjoint operators T ∈ A in terms of the spectra of the associated sequence of finite dimensional compressions PnTPn. In a suitable context, we showed that this is possible when Pn in...

Unitary Orbits of Normal Operators in Von Neumann Algebras

The starting points for this paper are simple descriptions of the norm and strong* closures of the unitary orbit of a normal operator in a von Neumann algebra. The statements are in terms of spectral data and do not depend on the type or cardinality of the algebra. We relate this to several known results and derive some consequences, of which we list a few here. Exactly when the ambient von Neu...

Localization for Random Unitary Operators

We consider unitary analogs of 1−dimensional Anderson models on l2(Z) defined by the product Uω = DωS where S is a deterministic unitary and Dω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of Uω is pure point almost surely for all val...

Unitary Invariants for Compact Operators

We describe in this note how the "boundary representation" technique introduced in [l ] leads to a complete classification of compact operators on Hubert spaces to unitary equivalence (Theorem 3), in terms of a sequence of invariants related to (and generalizing) the numerical range. These invariants are, we feel, vastly simpler than one might have anticipated in so general a situation. Full de...

Quadratic Forms in Unitary Operators