PG - TRB - MATHS MAJOR - FUNCTIONAL ANALYSIS - INTRODUCTION BASIC CONCEPT - UNIT - 5 - PART - 1

PG - TRB - MATHS MAJOR - FUNCTIONAL ANALYSIS - INTRODUCTION BASIC CONCEPT - UNIT - 5 - PART - 1

CONTACT : 9042030163

Unit V FUNCTIONAL ANALYSIS
Banach Spaces – Definition and examples – Holder’s inequality and Minkowski’s
inequality – Continuous linear transformations – The Hahn-Banach theorem –
Natural imbedding of X in X** – The Open mapping and The Closed graph
theorem – Properties of conjugate of an operator.
Hilbert spaces – Orthonormal bases – Conjugate space H* – Adjoint of an
operator – Projections – Matrices – Basic operations of matrices – Determinant
of a matrix – Determinant and Spectrum of an operator – Spectral theorem for
operators on a finite dimensional Hilbert space – Regular and Singular elements
in a Banach Algebra – Topological divisor of zero – Spectrum of an element in a
Banach algebra – The formula for the spectral radius – Radical and semi-simplicity.

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