Bounded Operators: Theory and Applications

Related lectures (31)

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

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

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

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

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

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

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

Explores linear operators, boundedness, and convergence in Banach spaces, focusing on Cauchy sequences and operator identification.

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

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