Microspectral analysis of quasinilpotent operators

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Details

Original languageEnglish
Pages (from-to)281-306
JournalBANACH CENTER PUBLICATIONS
Volume112
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed

Researchers

Research units

  • Polish Academy of Sciences

Abstract

We develop a microspectral theory for quasinilpotent linear operators Q (i.e., those with σ(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 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∈C.

ID: 16528289