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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Elements of Hilbert Spaces and Operator Theory (Hardcover, 1st ed. 2017)
Loot Price: R6,600
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Elements of Hilbert Spaces and Operator Theory (Hardcover, 1st ed. 2017)
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The book presents an introduction to the geometry of Hilbert spaces
and operator theory, targeting graduate and senior undergraduate
students of mathematics. Major topics discussed in the book are
inner product spaces, linear operators, spectral theory and special
classes of operators, and Banach spaces. On vector spaces, the
structure of inner product is imposed. After discussing geometry of
Hilbert spaces, its applications to diverse branches of mathematics
have been studied. Along the way are introduced orthogonal
polynomials and their use in Fourier series and approximations.
Spectrum of an operator is the key to the understanding of the
operator. Properties of the spectrum of different classes of
operators, such as normal operators, self-adjoint operators,
unitaries, isometries and compact operators have been discussed. A
large number of examples of operators, along with their spectrum
and its splitting into point spectrum, continuous spectrum,
residual spectrum, approximate point spectrum and compression
spectrum, have been worked out. Spectral theorems for self-adjoint
operators, and normal operators, follow the spectral theorem for
compact normal operators. The book also discusses invariant
subspaces with special attention to the Volterra operator and
unbounded operators. In order to make the text as accessible as
possible, motivation for the topics is introduced and a greater
amount of explanation than is usually found in standard texts on
the subject is provided. The abstract theory in the book is
supplemented with concrete examples. It is expected that these
features will help the reader get a good grasp of the topics
discussed. Hints and solutions to all the problems are collected at
the end of the book. Additional features are introduced in the book
when it becomes imperative. This spirit is kept alive throughout
the book.
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