Banach-Steinhaus Theorem

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The Closed Graph Theorem

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

Normed Spaces

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

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: Operator Definitions

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

Functional Analysis I: Norms and Bounded Operators

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

Functional Analysis I: Closed Operators

Explores closed operators in functional analysis, focusing on completeness, boundedness, and projections in Banach spaces.

Dual Spaces: Definitions and Properties

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

Linear Operators: Boundedness and Convergence

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

Essential Operators: Spectrum and Resolvent Set

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

Extension of Linear Transformations

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