Isometries on Banach Spaces

function spaces

Richard J. Fleming, James E. Jamison (Autoren)

Buch | Softcover

208 Seiten

2019
Chapman & Hall/CRC (Verlag)
978-0-367-39557-5 (ISBN)

Artikel merken

Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one.

Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras.

This treatment provides a clear account of historically important results, exposes the principal methods of attack, and includes some results that are more recent and some that are lesser known. Unique in its focus, this book will prove useful for experts as well as beginners in the field and for those who simply want to acquaint themselves with this area of Banach space theory.

Fleming, Richard J.; Jamison, James E.

Beginnings. Continuous Function Spaces--The Banach-Stone Theorem. The L(p) Spaces. Isometries of Spaces of Analytic Functions. Rearrangement Invariant Spaces. Banach Algebras. Bibliography. Index.

Erscheinungsdatum	30.09.2019
Reihe/Serie	Monographs and Surveys in Pure and Applied Mathematics
Sprache	englisch
Maße	156 x 234 mm
Gewicht	294 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-367-39557-6 / 0367395576
ISBN-13	978-0-367-39557-5 / 9780367395575
Zustand	Neuware