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 Holder 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. Contents: Basic Elements of Metric Topology; New Types of Function Spaces; Theory of Hilbert Spaces; Operators on Hilbert Spaces; Spectral Theory; Fredholm Theory (by Mirza Karamehmedovic). Key Features Offers a fast construction of the Lebesgue integrable functions. These mathematical objects are introduced as added limits for sequences of continuous functions and are thereby experienced by students as being no more mysterious than the real numbers constructed as limits of sequences of rational numbers. No compromises are made with respect to mathematical rigor Contains a comprehensive discussion of the question about existence of a Schauder basis in a Hilbert space and the relation of this question to the topological notion of separability Contains a complete treatment of the spectral theorem for compact, self-adjoint linear operators on separable Hilbert spaces Readership: Undergraduates in mathematical and physical sciences, and electrical and electronic engineering.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.

Title | : | Functional Analysis |

Author | : | Vagn Lundsgaard Hansen |

Publisher | : | World Scientific - 2006-01-01 |

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