Lectures related to Theory of Bounded Operators on Hilbert Space

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Essential Operators: Spectrum and Resolvent Set

Covers the essential concepts of adjoint operators, spectrum, and resolvent sets in operator theory.

Matrix Representation of Operators and Basis Transformation

Explores the matrix representation of operators and basis transformation in linear algebra.

Extension of Linear Transformations

Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.

Unitary Group and Spectral Types

Covers the proof of unitary group uniqueness and spectral types.

Functional Calculus: Operator Definition and Properties

Explores the definition and properties of the functional calculus for self-adjoint and bounded operators.

Self-Adjoint Operators

Covers the criteria for operators to be self-adjoint and the Friedrichs extension theorem.

Postulates of Quantum Mechanics

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

Linear Algebra: Vector Spaces & Operators

Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

Spectral Decomposition of Bounded Self-Adjoint Operators

Explores the spectral decomposition of self-adjoint operators on Hilbert spaces.

Unitary Minimal Models: Representation Theory Insights

Covers the representation theory of unitary minimal models and the Virasoro algebra.

Crash Course on Quantum Mechanics

Covers fundamental concepts in quantum mechanics, including vector spaces, superposition, observables, and inner product.

Adjoint of Linear Operators on Inner Product Spaces

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.

Essential Adjoints: Spectral Decomposition and Symmetric Operators

Explores spectral decomposition, essential self-adjointness, and symmetric operators in Hilbert spaces.

Functional Analysis I: Norms and Bounded Operators

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.

Functional Analysis I: Spectral Theorem

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.

Quantum Mechanics: Measurement

Covers the axioms of quantum mechanics and the measurement of quantities in a quantum system.

Quantum Mechanics: Postulates and Observables

Explains the postulates of quantum mechanics and the representation of observables by operators.

Bounded Operators: Theory and Applications

Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.