Functional Analysis: Banach and Hilbert Spaces

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Related lectures (30)

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Interpolation Spaces

Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.

Hilbert Spaces: Definition and Properties

Covers the definition and properties of Hilbert spaces, including the Cauchy-Schwarz inequality and norm definition.

Functional Analysis and Distribution Theory

Introduces functional analysis, distribution theory, topological vector spaces, and linear operators, emphasizing their importance in engineering applications.

Vector Spaces and Convergence

Covers vector spaces, compact sets, convergence, continuity, and uniqueness theorems.

Function Spaces and Hilbert Spaces

Introduces function spaces and Hilbert spaces, discussing inner product spaces and the importance of completeness in Hilbert spaces.

Functional Analysis I: Foundations and Applications

Covers the foundations of modern analysis, introductory functional analysis, and applications in MAB111.

Hilbert Spaces: Orthonormal Systems

Explores Hilbert spaces, orthonormal systems, and the Bessel inequality, emphasizing their properties and significance.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Vector Spaces and Topology

Covers vector spaces, topology, and proof methods like the pigeonhole principle in R^n.