A First Course in Functional Analysis

Orr Moshe Shalit

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English

Chapman & Hall/CRC
30 September 2020

Functional analysis & transforms; Mathematical physics

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.

By: Orr Moshe Shalit
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 367g
ISBN: 9780367658137
ISBN 10: 0367658135
Pages: 240
Publication Date: 30 September 2020
Audience: College/higher education , General/trade , Primary , ELT Advanced
Format: Paperback
Publisher's Status: Active

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.

Reviews for A First Course in Functional Analysis

A First Course in Functional Analysis by Orr Moshe Shalit is an excellent introduction to linear analysis. Its straightforward approach to the key ideas of the field, with special emphasis on Hilbert spaces, will be very much appreciated both by students and instructors. The book is suitable for advanced undergraduates and beginning graduate students who have had prior exposure to advanced calculus and linear algebra. I highly recommend this book to anyone teaching a first course in abstract analysis. -Jens Harlander, Boise State University