Lecture 8 of 46week-02
Bounded Operators
Prof. G. Ramesh · IIT Hyderabad
Credits and licence
- From
- Operator Theory, IIT Hyderabad (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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- Tweens profiles and older. How courses are placed
All the lectures
- Semi Inner product spaces
- Inner Product Spaces
- Parallelogram law
- Hilbert Spaces
- Orthogonality
- Projection Theorem
- Linear Operator
- Bounded Operators
- Norm of a linear operator
- Examples of bounded operators
- The Adjoint Operator
- The adjoint: Properties
- Closed range operators-1
- Closed range operators-2
- Self-adjoint Operators
- Normal operators
- Isometris and Unitaries
- Isometris and Unitaries
- Mutually Orthogonal Projections
- Invariant Subspaces
- Monotone Convergence Theorem
- Square root
- Polar decomposition
- Invertibility
- Spectrum
- Spectral Mapping Theorem
- Decomposition of spectrum
- Computing spectrum: Examples
- Approximate spectrum
- Approximate spectrum: Properties
- Numerical bounds
- Compact Operators
- Compact Operators; Properties
- Spectral Theorem: Compact Self-Adjoint Operators
- Spectral Theorem: Consequences
- Compact Normal Operators
- Compact Operators Singular value Decomposition
- Fredholm Alternative Theorem
- Orthogonal decomposition of self-adjoint operators
- Spectral family; Properties-I
- Lecture 5: Spectral family; Properties-II
- Spectral theorem Self adjoint Operators
- Spectral theorem Examples
- Spectral theorem: Consequences
- Continuous functional Calculus
- Spectral mapping theorem