Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: MSC category 13E05 ( Noetherian rings and modules )

 Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2004 (vol 56 pp. 742)

Jiang, Chunlan
 Similarity Classification of Cowen-Douglas Operators Let $\cal H$ be a complex separable Hilbert space and ${\cal L}({\cal H})$ denote the collection of bounded linear operators on ${\cal H}$. An operator $A$ in ${\cal L}({\cal H})$ is said to be strongly irreducible, if ${\cal A}^{\prime}(T)$, the commutant of $A$, has no non-trivial idempotent. An operator $A$ in ${\cal L}({\cal H})$ is said to a Cowen-Douglas operator, if there exists $\Omega$, a connected open subset of $C$, and $n$, a positive integer, such that (a) ${\Omega}{\subset}{\sigma}(A)=\{z{\in}C; A-z {\text {not invertible}}\};$ (b) $\ran(A-z)={\cal H}$, for $z$ in $\Omega$; (c) $\bigvee_{z{\in}{\Omega}}$\ker$(A-z)={\cal H}$ and (d) $\dim \ker(A-z)=n$ for $z$ in $\Omega$. In the paper, we give a similarity classification of strongly irreducible Cowen-Douglas operators by using the $K_0$-group of the commutant algebra as an invariant. Categories:47A15, 47C15, 13E05, 13F05
 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2016 : https://cms.math.ca/