Previous issue ·  Next issue ·  Most recent issue · All issues

# Journal of Operator Theory

Volume 52, Issue 1, Summer 2004  pp. 113-132.

Linear spans of unitary and similarity orbits of a Hilbert space operator

Authors K.R. Davidson (1) and L.W. Marcoux (2)
Author institution: (1) Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
(2) Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Summary:  In this note, we show that if a bounded linear operator $T$ acting on an infinite dimensional, separable, complex Hilbert space $\mathcal{H}$ is not of the form scalar plus compact, then every bounded linear operator on $\mathcal{H}$ can be written as a linear combination of $144 or fewer operators unitarily equivalent to$T$, as a linear combination of$6$or fewer operators similar to$T$, and as a sum of$8$or fewer operators similar to$T$. When$T$is not polynomially compact, the set of all sums of 2 operators similar to$T$is dense in$\mathcal{B}(\mathcal{H})$, while if$T$is polynomially compact, but not of the form scalar plus compact, then the set of sums of$3$operators similar to$T$is dense in$\mathcal{B}(\mathcal{H})\$.

Contents    Full-Text PDF