Microspectral analysis of quasinilpotent operators
Abstract
We develop a microspectral theory for quasinilpotent linear operators $Q$ (i.e., those with $\sigma(Q) = \{0}$) in a Banach space. When such $Q$ is not compact, normal, or nilpotent, the classical spectral theory gives little information, and a somewhat deeper structure can be recovered from microspectral sets in $\C$. Such sets describe, e.g., semigroup generation, resolvent properties, power boundedness as well as Tauberian properties associated to $zQ$ for $z \in \C$.
 Publication:

arXiv eprints
 Pub Date:
 November 2012
 arXiv:
 arXiv:1211.4790
 Bibcode:
 2012arXiv1211.4790M
 Keywords:

 Mathematics  Spectral Theory;
 47A10;
 47B06;
 47B10;
 47B60