Functional Analysis

Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view tu ...more

Introductory Functional Analysis with Applications
A Course in Functional Analysis
Functional Analysis
A Hilbert Space Problem Book (Graduate Texts in Mathematics, 19)
A Course in Operator Theory (Graduate Studies in Mathematics, Vol. 21)
Measure, integration, and functional analysis
Linear Functional Analysis (Springer Undergraduate Mathematics Series)
An Invitation to C*-Algebras (Graduate Texts in Mathematics 39)
Functional Analysis: An Introduction for Physicists
Elementary Functional Analysis (Graduate Texts in Mathematics, 253)
Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory (Mathematical Surveys and Monographs) (Mathematical Surveys and Monographs, 223)
A User's Guide to Operator Algebras
Quantum Mechanics and Quantum Field Theory: A Mathematical Primer
Fundamentals of the Theory of Operator Algebras. Volume IV
Local Quantum Physics: Fields, Particles, Algebras (Theoretical and Mathematical Physics)
Functional Analysis, Sobolev Spaces and Partial Differential ... by Haïm BrézisIntroductory Functional Analysis with Applications by Erwin KreyszigElements of the Theory of Functions and Functional Analysis by Андрей Николаевич КолмогоровMethods of Modern Mathematical Physics by Michael ReedAn Introduction to Banach Space Theory by Robert E. Megginson
Functional Analysis (MMath)
44 books — 6 voters

Real and Complex Analysis by Walter RudinTopology by James R. MunkresIntroductory Functional Analysis with Applications by Erwin KreyszigCounterexamples in Topology;Dover Books on Mathematics by Lynn Arthur SteenC*-Algebras and Operator Theory by Gerard J. Murphy
Mathematical Analysis
47 books — 13 voters

Paul R. Halmos
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me. ...more
Paul R. Halmos

I am looking for partners to study Algebraic geometry, algebraic topology, commutative algebra, …more
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