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Microspectral analysis of quasinilpotent operators

Volume 112 / 2017

Banach Center Publications 112 (2017), 281-306 MSC: 47A10, 47B06, 47B10. DOI: 10.4064/bc112-0-15

Abstract

We develop a microspectral theory for quasinilpotent linear operators $Q$ (i.e., those with $\sigma(Q) = \{0 \}$) in a Banach space. For such operators, the classical spectral theory gives little information. Deeper structure can be obtained from microspectral sets in $\mathbb C$ as defined below. Such sets describe, e.g., semigroup generation, various resolvent properties, power boundedness as well as Tauberian properties associated to $zQ$ for $z \in \mathbb C$.

Authors

• Jarmo MalinenDepartment of Mathematics and Systems Analysis
Aalto University
P.O.Box 11100
00076 Aalto, Finland
e-mail
• Olavi NevanlinnaDepartment of Mathematics and Systems Analysis
Aalto University
P.O.Box 11100
00076 Aalto, Finland
• Jaroslav ZemánekInstitute of Mathematics