Hilbert Space Compact Operators and the Trace Theorem [Paperback]

A virtually self-contained treatment of Hilbert space theory which is suitable for advanced undergraduates and graduate students.Assuming familiarity with linear algebra and advanced calculus, this self-contained treatment of Hilbert space theory leads to an elementary proof of the Lidskij trace theorem and an introduction to the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators.Assuming familiarity with linear algebra and advanced calculus, this self-contained treatment of Hilbert space theory leads to an elementary proof of the Lidskij trace theorem and an introduction to the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators.The aim of this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory leading to an elementary proof of the Lidskij trace theorem. The author assumes the reader is familiar with linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach.1. Preliminaries; 2. Orthogonality; 3. Isomorphisms and isometries; 4. Bounded linear operators; 5. Elementary spectral theory; 6. Self-adjoint operators; 7. Compact operators on Hilbert space; 8. Square roots; 9. The weak Weyl inequality; 10. HilbertSchmidt and trace class operators; 11. The Lidskij trace theorem; Bibliography. Retherford's book...is like a tour to the top of a mountain. Every step is devoted to the final goal, the trace formula...the book is written in a style which reveals the author's enthusiasm. Thus it could be good prpaganda for functional analysis...this is a remarkable book which forces the student to understand mathematics and to be careful. A. Pietsch, Mathematical Reviews