Lectures related to Non-Bounded Operators: Spectral Theory

Essential Operators: Spectrum and Resolvent Set

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

Linear Operators: Basis Transformation and Eigenvalues

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

Functional Calculus: Self-Adjoint Operators

Covers self-adjoint operators, Weyl criterion, and functional calculus in the context of symmetric operators and real spectrum.

Bounded Operators: Theory and Applications

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

Functional Analysis I: Norms and Bounded Operators

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

Quantum Mechanics: Postulates and Observables

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

Functional Analysis I: Operator Definitions

Introduces linear and bounded operators, compact operators, and the Banach space.

Essential Adjoints: Spectral Decomposition and Symmetric Operators

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

Dynamical Approaches to Spectral Theory of Operators

Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.

Functional Analysis I: Spectral Theorem

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

Semigroups of Linear Operators

Explores semigroups of linear operators, contraction semigroups, infinitesimal generator, and Riemann integral properties.

Functional Calculus: Operator Definition and Properties

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

Compositions and adjoints of unbounded operators

Covers the fundamental concepts of unbounded operators and their adjoints, exploring auto-adjoint and normal operators.

The Closed Graph Theorem

Explores the Banach-Steinhaus theorem and the Closed Graph Theorem.

Dual Spaces: Definitions and Properties

Covers the definitions and properties of dual spaces and linear operators.

Quantum Measurement Postulate

Explores the verification of PVM properties and the spectral theorem for unbounded operators in quantum mechanics.

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.

Linear Operators: Quantum Mechanics and Linear Algebra

Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.

Spectral Decomposition of Bounded Self-Adjoint Operators

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

Spectral Decomposition of Unbounded Operators

Explores the spectral decomposition of non-bounded operators and presents the spectral theorem for self-adjoint non-bounded operators.