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Graduate Texts in Mathematics #96
A Course in Functional Analysis
This book is an introductory text in functional analysis, aimed at the graduate student with a firm background in integration and measure theory. Unlike many modern treatments, this book begins with the particular and works its way to the more general. The student will also appreciate the large number of examples and exercises which have been included.
400 pages, Hardcover
First published January 1, 1984
9 people are currently reading
115 people want to read
About the author
John B. Conway
24 books2 followersJohn B. Conway is a Professor of Mathematics at George Washington University.
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Displaying 1 - 4 of 4 reviews
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August 14, 2022Read this (mostly) in full to prepare for my PhD candidacy exam- highly prefer this to a functional analysis text like Rudin's (as an example). I wasn't completely blown away by the coverage of topological vector spaces and locally convex spaces, but it wasn't too much of an issue.
December 9, 2022
This is honestly a 4.5 star review, but I round down as the text is not perfect. With that said, this is a fantastic text to introduce one to Functional Analysis. There are some oddities with definitions, especially when the book gets into Topological Vector Spaces, but besides that, the book is very user friendly. I definitely enjoyed learning from it.
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January 8, 20242. The adjoint of an operator
Analogy: Taking the adjoint of an operator is analogous to taking the conjugate of a complex number.
(But, DOT NOT BECOME TOO RELIGIOUS ABOUT IT!)
Definition 2.11. If A:H->H bounded then: A is hermitian or self-adjoint if A=A^*, A is normal if AA^*=A^*A.
Analogy: A self-adjoint analogous to z=conjugate{z} (this implies that z is a real number)
A unitary operator analogous of complex numbers of modulus 1
Normal operators analogous complex numbers
Chapter VII Banach algebras and Spectral theory for operators on a Banach space.
Example: If X is a Banach space, then B(X) is a Banach algebra (with multiplication and composition with identity 1)
Analogy: Taking the adjoint of an operator is analogous to taking the conjugate of a complex number.
(But, DOT NOT BECOME TOO RELIGIOUS ABOUT IT!)
Definition 2.11. If A:H->H bounded then: A is hermitian or self-adjoint if A=A^*, A is normal if AA^*=A^*A.
Analogy: A self-adjoint analogous to z=conjugate{z} (this implies that z is a real number)
A unitary operator analogous of complex numbers of modulus 1
Normal operators analogous complex numbers
Chapter VII Banach algebras and Spectral theory for operators on a Banach space.
Example: If X is a Banach space, then B(X) is a Banach algebra (with multiplication and composition with identity 1)
Currently reading
May 10, 2018I want to read this book. Anyone interested in joining me to study together, let me know. We can also look for expository work afterwards. Just message me.
Displaying 1 - 4 of 4 reviews