Bounded operator

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Related lectures (32)

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Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Signal Representations

Covers the norm of a matrix, operator, singular values, and unitary matrices in linear algebra.

Distributional Derivatives

Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.

Functional Analysis I: Spectral Theorem

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

Sequences: Definitions and Examples

Covers solving equations over complex numbers, sequences, induction, and properties of complex numbers.

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Fundamental Solutions of Laplace Equation

Covers the fundamental solutions of the Laplace equation and introduces distributions.

Resolving Operators: Closedness and Injectivity

Discusses resolving operators' closedness and injectivity in Banach spaces.

Derivable Functions: Limits and Continuity

Explores derivable functions, limits, continuity, and differentiability, emphasizing the relationship between them.

Quantum Mechanics: Mathematical Framework

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.