Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.

• 1: Decomposable operators


• 2: Functional models, duality theory, and invariant subspaces


• 3: The spectrum and spectral inclusions


• 4: Local spectral theory for multipliers


• 5: Connections to automatic continuity


• 6: Open problems


• Appendix


• Bibliography


• Index of notation


• Index

Kjeld Bagger Laursen Department of Mathematics University of Copenhagen Universitetsparken 5 DK-2100 COPENHAGEN, DENMARK Tel. +45 35320690 Fax: +45 35320704 Email: laursen@math.ku.dk Michael M Neumann Department of Mathematics and Statistics Mississippi State University P.O. Drawer MA Mississippi State, MS 39762 USA Tel.: +1 662 325-3414 Fax.: +1 662 325-0005 Email: neumann@math.msstate.edu