The material presented in this book is suited for a first course in
Functional Analysis which can be followed by masters students.
While covering all the standard material expected of such a course,
efforts have been made to illustrate the use of various theorems
via examples taken from differential equations and the calculus of
variations, either through brief sections or through exercises. In
fact, this book will be particularly useful for students who would
like to pursue a research career in the applications of
mathematics. The book includes a chapter on weak and
weak*topologies and their applications to the notions of
reflexivity, separability and uniform convexity. The chapter on the
Lebesgue spaces also presents the theory of one of the simplest
classes of Sobolev spaces. The book includes a chapter on compact
operators and the spectral theory for compact self-adjoint
operators on a Hilbert space. Each chapter has large collection of
exercises at the end. These illustrate the results of the text,
show the optimality of the hypotheses of various theorems via
examples or counterexamples, or develop simple versions of theories
not elaborated upon in the text.
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