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A Short Course on Spectral Theory - Graduate Texts in Mathematics Vol.209(2002)  무료배송

 
지은이 : William Arveson
출판사 : Springer-Verlag
판수 : first edition
페이지수 : 136
ISBN : 0387953000
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 85,000원 ( 무료배송 )
적립금 : 2,550 Point
     

 
This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative k-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here. The book is based on a fifteen-week course which the author offered to first or second year graduate students with a foundation in measure theory and elementary functional analysis.
1. Spectral Theory and Banach Algebras
2. Operators on Hilbert Space
3. Asymptotics: Compact Perturbations and Fredholm Theory
4. Methods and Applications
"The word "spectrum" comes from quantum theory, as does the
subject of operators in Hilbert space. Since the early days, the
subject has grown, and branched out in a variety of directions.
This fact has perhaps made it difficult for an instructor to
chose a book from which to teach the fundamental ideas;--
those ideas in a subject that stay constant, even when the
fashions change. The topics covered in Arveson's book are relevant now, and are likely to
be useful decades from now. They are beautifully presented.--
The material and the format have been tested in courses;-- and this book represents a formula that works!"


"You can find the same material in a bunch of books... but the exposition by Arveson is really superb. He actually EXPLAINS things, not just a list of theorems and proofs with no apparent reason.

The book is 130p only, so it might be ideal for self study. Not everything is in the text but if you want to try the exercises (you might need further reading to do some of them) and you do the extra reading from other sources, you will end up getting a good understanding.

The chapters are: 1. Spectral theory and Banach algebras, 2. Operators on Hilbert space, 3. Asymptotics: Compact perturbations and Fredholm theory and 4. Methods and applications

approximatelly 170 exercises.

The most inspiring book on the subject I have seen, up to now."

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