MATH 5831

MATH 5831 Advanced Functional Analysis 4(3+1) credit hours
Spectrum of an operator, compact linear operators and their spectral properties, spectral properties of bounded self-adjoint operators, positive operators, product of positive operators, square root of positive operator, projection operators: Theorem (positivity, norm), Theorem (partial order), Theorem (product of projections), Theorem ( sum of projections), Theorem (difference of projections), Spectral family of a bounded self-adjoint operator, Banach algebras, Gelfand’ mapping, spectral theorem for normal operators.
References:
1- Kreyszig E., Introductory functional analysis with applications, New York : Wiley, 1989, ©2006
2- Simmons G. F. , Introduction to Topology and Modern Analysis, (International student Edition), McGraw-Hill, 1983.