Description

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.

Functional Analysis: Entering Hilbert Space

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Paperback / softback by Vagn Lundsgaard Hansen

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This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof... Read more

    Publisher: World Scientific Publishing Co Pte Ltd
    Publication Date: 22/05/2006
    ISBN13: 9789812566867, 978-9812566867
    ISBN10: 9812566864

    Number of Pages: 148

    Non Fiction , Mathematics & Science , Education

    Description

    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.

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