AM 302 : FUNCTIONAL ANALYSIS (Common with paper MA 302 of Branch I(A) Mathematics) UNIT : –I The definitions and some examples transformations-the –continuous –linear Theorem. UNIT II: – Natural imbedding of N in N**-Open mapping theorem of an Operator. –Conjugate UNIT III: – Definition and Simple Properties Complements- Orthonormal sets –Orthogonal – Conjugate spaces-Adjoint of an Operator. UNIT-IV: Self adjoint operators and Unitary Operators-Projection theorem. –Normal –Spectral Scope and Standard as in Sections 46 to 51 of Chapter 9, section 52 to 59 of chapter 10, section 62 of chapter 11 of Introduction to Topological and Modern analysis by “ G.F. Simmons Mc Graw Hill Book Company. References : 1. Foundations of Functional by S. Ponnusamy-Narosa “ Analysis” Publications 2. Text book of Functional Analysis A “ – Problem oriented Approach” by V.K. Krishnan-Prentice Halls of India Publishers 3. Functional by B.V. Limaye New age International “ Analysis” Publishers
AM 302 : FUNCTIONAL ANALYSIS (Common with paper MA 302 of Branch I(A) Mathematics) UNIT –I : The definitions and some examples –continuous –linear transformations-the Theorem. UNIT – II: Natural imbedding of N in N**-Open mapping theorem –Conjugate of an Operator. UNIT – III: Definition and Simple Properties –Orthogonal Complements- Orthonormal sets – Conjugate spaces-Adjoint of an Operator. UNIT-IV: Self adjoint operators –Normal and Unitary Operators-Projection –Spectral theorem. Scope and Standard as in Sections 46 to 51 of Chapter 9, section 52 to 59 of chapter 10, section 62 of chapter 11 of “ Introduction to Topological and Modern analysis by G.F. Simmons Mc Graw Hill Book Company. References : 1. “ Foundations of Functional Analysis” by S. Ponnusamy-Narosa Publications 2. “ Text book of Functional Analysis – A Problem oriented Approach” by V.K. Krishnan-Prentice Halls of India Publishers 3. “ Functional Analysis” by B.V. Limaye New age International Publishers