Banach Space Complexes: 334 (Mathematics and Its Applications, 334) - Hardcover

Ambrozie, C.-G.; Vasilescu, Florian-Horia

Hardcover

ISBN 10: 0792336305 ISBN 13: 9780792336303

Publisher: Springer, 1995

Synopsis

The aim of this work is to initiate a systematic study of those properties of Banach space complexes that are stable under certain perturbations. A Banach space complex is essentially an object of the form 1 op-l oP +1 ... --+ XP- --+ XP --+ XP --+ ... , where p runs a finite or infiniteinterval ofintegers, XP are Banach spaces, and oP : Xp ..... Xp+1 are continuous linear operators such that OPOp-1 = 0 for all indices p. In particular, every continuous linear operator S : X ..... Y, where X, Yare Banach spaces, may be regarded as a complex: O ..... X ~ Y ..... O. The already existing Fredholm theory for linear operators suggested the possibility to extend its concepts and methods to the study of Banach space complexes. The basic stability properties valid for (semi-) Fredholm operators have their counterparts in the more general context of Banach space complexes. We have in mind especially the stability of the index (i.e., the extended Euler characteristic) under small or compact perturbations, but other related stability results can also be successfully extended. Banach (or Hilbert) space complexes have penetrated the functional analysis from at least two apparently disjoint directions. A first direction is related to the multivariable spectral theory in the sense of J. L.

About this title

Synopsis

This text offers a systematic approach to the study of those properties of Banach space complexes that are stable under certain perturbations. The stability of the index under small or compact perturbations is presented within the context of (semi-)Fredholm complexes. Various invariants and other properties are also considered. This raises certain problems requiring further study of more general Fredholm-type objects. Some of the results are new. Applications in several variables spectral theory and in other related fields are also given. The book should be of interest to graduate students and specialists in functional analysis, operator theory, integral transforms, operational calculus, partial differential equations and several complex variables.

Edition details

• Publisher: Springer
• Publication date: 1995
• Language: English
• ISBN 10: 0792336305
• ISBN 13: 9780792336303
• Binding: Hardcover
• Number of pages: 218