Leo Livshits - Locally linearly dependent spaces of matrices

Portal

Donate

FranÃ§ais

Next: V. Lomonosov - Density Up: Operator Theory / Théorie Previous: Michael P. Lamoureux -

Leo Livshits - Locally linearly dependent spaces of matrices

	LEO LIVSHITS, Colby College, Waterville, Maine 04901, USA
	Locally linearly dependent spaces of matrices

(Joint work with D. Hadwin and B. Mathes)

A subspace $\Psi$ of ${M}_{m\times n}({\bf C})$ is said to be locally linearly dependent (``LLD'') if $\{T(x)\mid T\in \Psi \}$ is linearly dependent for every $x \in {\bf F}^n$ . Locally linearly independent (i.e. not dependent) spaces are exactly those possessing a separating vector. If such a space is proper and does not have a one-dimensional $\textrm{LLD}$ extention, then it is reflexive. (Converse is false.)

We will present several results about $\textrm{LLD}$ spaces. For example: no $\textrm{LLD}$ subspace of $M_{n}({\bf C})$ , $n\geq 3$ can contain both an invertible and a cyclic operator.

eo@camel.math.ca

Canadian Mathematical Society
616 Cooper St.
Ottawa, ON K1R 5J2, Canada
Telephone: +1 (613) 733-2662

Detailed contact information

Privacy information

Copyright & Permissions
The Canadian Mathematical Society grants permission to individual readers of this publication to copy articles for their own personal use. Use for any other purpose is strictly prohibited. To obtain a license for anything other than copying articles for personal use, please contact the Canadian Mathematical Society to request permissions or licensing terms.

Canadian Mathematical Society — 616 Cooper St., Ottawa, ON K1R 5J2, Canada