Symmetric invariant subspaces of complexifications of linear operators

Invariant Subspaces, Quasi-invariant Subspaces, and Hankel Operators

In this paper, using the theory of Hilbert modules we study invariant subspaces of the Bergman spaces on bounded symmetric domains and quasi-invariant sub-spaces of the Segal–Bargmann spaces. We completely characterize small Hankel operators with finite rank on these spaces.

Lie-algebras and Linear Operators with Invariant Subspaces

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with the above property must have a representation as a polynomial element of the universal enveloping algebra of some algebra of differential (difference) opera...

Linear Algebra: Invariant Subspaces

Introduction 1 1. Invariant Subspaces 3 2. Eigenvectors, Eigenvalues and Eigenspaces 11 3. Cyclic Spaces 14 4. Prime and Primary Vectors 15 5. The Cyclic Decomposition Theorem 20 6. Rational and Jordan Canonical Forms 22 7. Similarity 23 8. The Cayley-Hamilton Polynomial (Or: Up With Determinants?) 24 9. Extending The Ground Field 25 9.1. Some Invariances Under Base Extension 25 9.2. Semisimpli...

Invariant subspaces of abstract multiplication operators

INVARIANT SUBSPACES OF ABSTRACT MULTIPLICATION OPERATORS by Hermann Flaschka We describe a class of operators on a Banach space ft whose members behave, in a sense, like multiplication operators, and consequently leave invariant a proper closed subspace of IB. One of the sufficient conditions for an operator to be such an "abstract multiplication" bears a striking resemblence to an assumption m...

Doubly Invariant Subspaces of Annulus Operators