Description
A First Course in Functional Analysis
Author: Shalit Orr Moshe
Language: English
Subjects for A First Course in Functional Analysis:
Keywords
Stone Weierstrass theorem; Hilbert spaces; Fourier Series; Bounded functionals and Bounded operators; Banach spaces; Riesz theorem; operator theory; metric spaces; functional analysis; Riemann integration; Hilbert space methods; Hilbert Space; Multiplier Algebra; Infinite Dimensional Banach Space; Hamel Basis; Banach Space; Finite Dimensional Normed Space; Compact Operator; Finite Rank Operator; Piecewise Continuous Map; Nice Functions; Orthonormal Basis; Finite Dimensional Spaces; Metric Space; Normed Spaces; Hilbert Function Space; Complete Orthonormal System; Hahn Banach Extension Theorem; Compact Self-adjoint Operator; Infinite Dimensional Vector Space; Isometrically Isomorphic; Orthonormal System; Closed Subspace; Hahn Banach Theorem
Publication date: 09-2020
· 15.6x23.4 cm · Paperback
Publication date: 03-2017
· 15.6x23.4 cm · Hardback
Description
/li>Contents
/li>Biography
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Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside real applications in analysis. The background required for a student taking this course is minimal; basic linear algebra, calculus up to Riemann integration, and some acquaintance with topological and metric spaces.
Introduction and the Stone-Weierstrass theorem. Hilbert spaces. Orthogonality, projections, and bases. Fourier series. Bounded linear operators on Hilbert space. Hilbert function spaces. Banach spaces. The algebra of bounded operators on a Banach space. Compact operators. Compact operators on Hilbert space. Applications of compact operators. The Fourier transform. *The Hahn-Banach Theorems. Metric and topological spaces.
Orr Moshe Shalit is an assistant professor of mathematics at the Technion - Israel Institute of Technology in Haifa, Israel. His research interests lie in the topic of operator theory and operator algebras. He is the author of over 20 research papers and is a regular reviewer for many prestigious journals.