## Texts and Readings in Mathematics

Notes on Functional Analysis

Rajendra Bhatia

The book is organised as twenty six lectures, each corresponding to a ninety minute class session. This may be helpful to teachers planning a course on this topic. Well prepared students can read it on their own.

Contents

2: Dimensionality

3: New Banach Spaces from Old

4: The Hahn-Banach Theorem

5: The Uniform Boundedness Principle

6: The Open Mapping Theorem

7: Dual Spaces

8: Some Applications

9: The Weak Topology

10: The Second Dual and the Weak* Topology

11: Hilbert Spaces

12: Orthonormal Bases

13: Linear Operators

14: Adjoint Operators

15: Some Special Operators in Hilbert Space

16: The Resolvent and The Spectrum

17: Subdivision of the Spectrum

18: Spectra of Normal Operators

19: Square Roots and the Polar Decomposition

20: Compact Operators

21: The Spectrum of a Compact Operator

22: Compact Operators and Invariant Subspaces

23: Trace Ideals

24: The Spectral Theorem –I

25: The Spectral Theorem –II

26: The Spectral Theorem –III

Index

Texts and Readings in Mathematics/ 50

Reprint 2015, 9789380250793,248 pages, papercover, Rs: 450.00

Reprint 2015, 9789380250793,248 pages, papercover, Rs: 450.00