FUNCTIONAL ANALYSIS

WEEK No.

Chapter No.

Chapter Name 

Module

Module Name

Week 1

1

Metric Spaces

1

Fundamental Inequalities

2

Some Properties On Metric Spaces

3

Metric Subspaces

Week 2

2

Fundamental Theorems For Metric Spaces

1

Completion Of Metric Spaces

2

Compactness Of c[a,b]

3

Fixed Point Of Contraction Mappings

Week 3

3

Normed Linear Spaces and Banach Spaces

1

Linear Spaces

2

Basic Properties Of A Normed Linear Space

3

Examples Of Banach Spaces

Week 4

3

Normed Linear Spaces And Banach Spaces

4

Some Important Results On Normed Linear Spaces and Banach spaces

4

Characterization Of Banach Spaces

1

Convex Sets

2

Equivalent Norms And Series In Banach spaces

Week 5

4

Characterization Of Banach Spaces

3

Quotient Spaces

5

Bounded Linear Operators

1

Basic Results On Bounded Linear Operators

2

Norm Of Bounded Linear Operators

Week 6

5

Bounded Linear Operators

3

Convergence Of Bounded Linear Operators

6

Fundamental Theorems For Bounded Linear Operators

1

Open Mapping Theorem

Week 7

6

Fundamental Theorems for Bounded Linear Operators

2

Closed Graph Theorem

3

Extension Of Bounded Linear Operators

Week 8

Revision and Assignment Week 

Week 9

7

Fundamental Theorems For Bounded Linear Functionals

1

Linear Functionals

2

Hahn Banach Theorem

3

Applications Of Hahn Banach Theorem

Week 10

8

Conjugate Spaces

1

First Conjugate Spaces

2

Second Conjugate spaces

3

Strong Convergence And Weak Convergence Of A Sequence Of Operators

Week 11

8

Conjugate Spaces

4

Conjugate Operators On Normed Linear Spaces

Week 11

9

Inner Product Spaces And Hilbert Spaces

1

Inner Product Spaces

2

Orthogonal And Orthonormal Vectors

Week 12

9

Inner Product Spaces And Hilbert Spaces

3

Some Fundamental Results On Inner Product Spaces

4

Some Results On Hilbert Spaces

Week 13

9

Inner Product Spaces And Hilbert spaces

5

Series In Hilbert Spaces And Isometric Isomorphism Between Hilbert spaces

10

Classification Of Operators Over Hilbert Spaces

1

Adjoint Operators And Algebra Of Adjoint Operators

Week 14

10

Classification Of Operators Over Hilbert Spaces

2

Self Adjoint Operators Over Hilbert Spaces And Its Eigen Values And Eigen Vectors

3

Normal Operators And Unitary Operators

4

Projection Operators

Week 15

Assessment and overview of the course