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Functional Analysis: Entering Hilbert Space (Hardcover, Second Edition)
Loot Price: R1,536
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Functional Analysis: Entering Hilbert Space (Hardcover, Second Edition)
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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 Hoelder 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.In this second edition, I have expanded the material on
normed vector spaces and their operators presented in Chapter 1 to
include proofs of the Open Mapping Theorem, the Closed Graph
Theorem and the Hahn-Banach Theorem. The material on operators
between normed vector spaces is further expanded in a new Chapter
6, which presents the basic elements of the theory of Fredholm
operators on general Banach spaces, not only on Hilbert spaces.
This requires that we develop the theory of dual operators between
Banach spaces to replace the use of adjoint operators between
Hilbert spaces.With the addition of the new material on normed
vector spaces and their operators, the book can serve as a general
introduction to functional analysis viewed as a theory of infinite
dimensional linear spaces and linear operators acting on them.
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