http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
On the structure of a class of operators
In this dissertation we study certain classes of operators on a separable, complex ,infinite dimensional Hilbert space H, specifically from the point of view of properties of the hyperlattice (i.e., lattice of hyperinvariant subspaces) for such operators. We show that every (BCP)-operator in C₀₀ is hyperquasisimilar to a quasidiagonal (BCP)-operator in C₀₀. Moreover we show that there exists a fixed block diagonal (BCP)-operator B[subscript]u with the property that if every compact perturbation B[subscript]u + K of B[subscript]u in(BCP) and C₀₀ with llKll< [E] has a nontrivial hyperinvariant subspace, then every nonscalar operator on H has a nontrivial hyperinvariant subspace. This shows that the study of the structure of the hyperlattice of an arbitrary operator on Hilbert space is essentially equivalent to the study of the hyperlattice structure of some much smaller, special classes of operators, and it is these on which we concentrate. Moreover, we study some special subclasses (B[theta]) and (S[theta]) of the class of in-vertible (BCP)-operators with a view of obtaining some insight into the problem of determining the structure of operators in these classes.
Title from author supplied metadata (automated record created on Sep. 21, 2005.)
System requirements: World Wide Web access and Adobe Acrobat Reader.