This text is the first of its kind exclusively devoted to
counterexamples in operator theory and includes over 500 problems
on bounded and unbounded linear operators in Hilbert spaces. This
volume is geared towards graduate students studying operator
theory, and the author has designated the difficulty level for each
counterexample, indicating which ones are also suitable for
advanced undergraduate students. The first half of the book focuses
on bounded linear operators, including counterexamples in the areas
of operator topologies, matrices of bounded operators, square
roots, the spectrum, operator exponentials, and non-normal
operators. The second part of the book is devoted to unbounded
linear operators in areas such as closedness and closability,
self-adjointness, normality, commutativity, and the spectrum,
concluding with a chapter that features some open problems.
Chapters begin with a brief “Basics” section for the readers’
reference, and many of the counterexamples included are the
author’s original work. Counterexamples in Operator Theory
can be used by students in graduate courses on operator theory and
advanced matrix theory. Previous coursework in advanced linear
algebra, operator theory, and functional analysis is assumed.
Researchers, quantum physicists, and undergraduate students
studying functional analysis and operator theory will also find
this book to be a useful reference.
General
Imprint: |
Springer Nature Switzerland AG
|
Country of origin: |
Switzerland |
Release date: |
May 2023 |
Firstpublished: |
2022 |
Authors: |
Mohammed Hichem Mortad
|
Dimensions: |
235 x 155mm (L x W) |
Pages: |
598 |
Edition: |
1st ed. 2022 |
ISBN-13: |
978-3-03-097816-7 |
Categories: |
Books
|
LSN: |
3-03-097816-8 |
Barcode: |
9783030978167 |
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