Precize Functional Analysis


The entire subject matter in the present book has been arranged in a simple, systematic, graded, lucid and exhaustive manner. Each chapter begins with definitions followed by theorems with complete proofs and solved problems. A large number of notes and remarks have been added for better understanding of the subject. For UGC-CSIR NET examination, some MCQ’s from the previous years papers and other similar questions have been added at the end of the book.


Banach Spaces with examples of ([a, b]) and C([a, b]), Hahn Banach theorem, open mapping theorem, closed graph theorem, Baire Category theorem, Banach Steinhauns theorem (uniform boundedness principle), Boundedness and continuity of linear transformation, Dual Spaces, embedding in second dual.

       Hilbert space, orthonormal basis, Bessel’s inequality, Riesz Fischer theorem, Parseval’s identity, bounded Linear functionals; projections, Riesz Representation theorem, adjoint operators, self adjoint, normal, unitary and isometric operators.

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