Introduction to Local Spectral Theory (Hardcover)

Hardcover. 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, whose pioneers include Dunford, Bishop, Foias, and others. Assuming only modest prerequisites of its readership, it gives complete coverage of the field, including the fundamental recent work byAlbrecht and Eschmeier which provides the full duality theory for Banach space operators. It is highlighted by many characterizations of decomposable operators, and of other related, important classes ofoperators, as well as an in-depth study of their spectral properties, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Also found is a thorough and quite elementary treatment of the modern single- operator duality theory; this theory has many applications, both to general issues of classification and to such celebrated problems as the invariant subspace problems. A long chapter - almost a book initself - is devoted to the use of local spectral theory in the study of spectral properties of multipliers and convolution operators. Another one describes its connections to automatic continuity theory.Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, and extensive references. It concludes with a list of interesting open problems, suitable for continued research. This book is a modern treatment of a classical area of operator theory. Written in a meticulous and detailed style, with the modern graduate student of analysis in mind, it contains many simplifications of existing literature. It is full of new results, as well as many illuminating examples. Carefully cross referenced throughout, it also includes an extensive list of the relevant literature. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…