Functional Analysis: Entering Hilbert Space
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A01=Vagn Lundsgaard Hansen
Author_Vagn Lundsgaard Hansen
Category=PBKF
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eq_nobargain
Fredholm Theory
Hilbert Spaces
Lebesgue Integrable Functions
Operators on Hilbert Spaces
Spectral Theory
Product details
- ISBN 9789812566867
- Publication Date: 22 May 2006
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Paperback
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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.
