Genre
- Journal Article
It is Shown that a nest in a Hilbert space H is the lattice of closed invariant subspaces of a band algebra in B(H) (i.e. an algebra generated by a semigroup of idempotent operators) if and only if all finite-dimensional atoms of the nest have dimension 1. A canonical operator matrix form for operator bands, developed by the authors, is used to demonstrate that the set of algebraic operators in B(H) coincides with the union of all band subalgebras of B(H). Several sufficient conditions for an operator band to be reducible and triangularizable are presented, and a new proof is given for a theorem on algebraic triangularizability of arbitrary operator bands.
Colby Coll, Dept Math, Waterville, ME 04901 USA. Univ Prince Edward Isl, Dept Math & CS, Charlottetown, PE C1A 4P3, Canada. Dalhousie Univ, Dept Math Stat & Comp Sci, Halifax, NS B3H 3J3, Canada.; Livshits, L, Colby Coll, Dept Math, Waterville, (TRUNCATED)
BUCHAREST; C/O INST MATHEMATICS, PO BOX 1-764, BUCHAREST 70700, ROMANIA
THETA FOUNDATION
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Source type: Electronic(1)
Language
- English
Subjects
- OPERATORS
- reducible
- idempotents
- semigroups
- Mathematics
- invariant subspaces
- bands
- SPECTRAL CONDITIONS
- irreducible representations