FUNCTIONAL ANALYSIS: ENTERING HILBERT SPACE - Hardcover

Hansen, Vagn Lundsgaard

Hardcover

ISBN 10: 9812565639 ISBN 13: 9789812565631

Publisher: World Scientific Publishing Company, 2006

Synopsis

This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of Hölder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.

About this title

Review

The highlight of the book is the spectral theorem for selfadjoint linear compact operators, presented with full proof. The book ends with a set of well chosen exercises completing the main text.

Edition details

• Publisher: World Scientific Publishing Company
• Publication date: 2006
• Language: English
• ISBN 10: 9812565639
• ISBN 13: 9789812565631
• Binding: Hardcover
• Number of pages: 148