Introduction to Functional Analysis by University of Leeds
Introduction to Functional Analysis by University of Leeds
Introduction to Functional Analysis by University of Leeds
This PDF book covers the following topics
related to Functional Analysis :Basics of Metric Spaces, Basics of Linear
Spaces, Orthogonality, Duality of Linear Spaces, Fourier Analysis, Operators,
Spectral Theory, Compactness, The spectral theorem for compact normal operators,
Banach and Normed Spaces, Measure Theory, Integration, Functional Spaces,
Fourier Transform, Advances of Metric Spaces.
Author(s): Vladimir V. Kisil, School of
Mathematics, University of Leeds
Functional analysis plays an important
role in the applied sciences as well as in mathematics itself. These notes are intended to familiarize the student with the basic
concepts, principles andmethods of functional analysis and its applications, and
they are intended for senior undergraduate or beginning graduate students.
Topics covered includes: Normed and Banach spaces, Continuous maps,
Differentiation, Geometry of inner product spaces , Compact operators and
Approximation of compact operators.
This note explains
the following topics: Metric and topological spaces, Banach spaces, Consequences
of Baire's Theorem, Dual spaces and weak topologies, Hilbert spaces, Operators
in Hilbert spaces, Banach algebras, Commutative Banach algebras, and Spectral
Theorem.