Equivalence of Decomposability and 2-Decomposability for Several Commuting Operators.
Bishop's condition (ß) and joint invariant subspaces.
Tensor products and elementary operators.
Operators with rich invariant subspace lattices.
Spectral Decompositions and Decomposable Multipliers.
Local Properties of Taylor's Analytic Functional Calculus.
Representations of H...(G) and invariant subspaces.
Fredholm spectrum and growth of cohomology groups
Let T ∈ L(E)ⁿ be a commuting tuple of bounded linear operators on a complex Banach space E and let be the non-essential spectrum of T. We show that, for each connected component M of the manifold of all smooth points of , there is a number p ∈ 0, ..., n such that, for each point z ∈ M, the dimensions of the cohomology groups grow at least like the sequence with d = dim M.
The essential spectrum of Toeplitz tuples with symbols in
Let H²(D) be the Hardy space on a bounded strictly pseudoconvex domain D ⊂ ℂⁿ with smooth boundary. Using Gelfand theory and a spectral mapping theorem of Andersson and Sandberg (2003) for Toeplitz tuples with -symbol, we show that a Toeplitz tuple with symbols is Fredholm if and only if the Poisson-Szegö extension of f is bounded away from zero near the boundary of D. Corresponding results are obtained for the case of Bergman spaces. Thus we extend results of McDonald (1977) and Jewell (1980)...
Spectral theory and sheaf theory. III.
A commutant lifting theorem on analytic polyhedra
In this note a commutant lifting theorem for vector-valued functional Hilbert spaces over generalized analytic polyhedra in ℂⁿ is proved. Let T be the compression of the multiplication tuple to a *-invariant closed subspace of the underlying functional Hilbert space. Our main result characterizes those operators in the commutant of T which possess a lifting to a multiplier with Schur class symbol. As an application we obtain interpolation results of Nevanlinna-Pick and Carathéodory-Fejér type...
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