| My Favorite Books |
| C* lagebras and their Automorphism Groups
by G.K.Pedersen | |
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In the late of 1970's, Takesaki,Pedersen,and
Bratelli had written three big books independently in
highly sophisticated style. This is one of great and
difficult books which I have ever tried. Still, I have to read it! Reference for Good matereials for C* crossed product. |
| C*algebra and their representations/Von Neumann Algebra by J.Dixmier | |
| It shows the technique of representation
of C*algebra for the study of C*algebra. The author presents a
comprehensive introduction to general theory of C*algebra. Some definitions
and terminologies become too old. Refernce for A continous field of Hilbert spaces/ A continous field of C* algebras/ C*algebra derived from a continous field. |
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| Operator algebra and its application to quantum statistical mechanics by O.Bratelli | |
| This book contains the proof of Tomita-Takesaki modular theory, which is comparatively easy. | |
| Lectures on Von Neumann Algebra by D.M.Topping | |
| This thin book shows a smooth introduction to von Nuemann Algebra and supplies necessary materials for further study. | |
| C*algebra by examples by K.Davidson | |
| Until 1980's the study of operator algebra was focused on various structure theories mainly. So, only top-class mathematicians continued to pioneer the area. The direction of research was changed little by little , however, many specific examples of operator algebra each of which is important of its own and interelated to other areas of mathematics-specially topology and geometry have been found by famous mathematicians. | |
| Principles of Functional Analysis by M.Schecter | |
| This book is the best text for beginnig graduate student who wish to learn the basics of functional analysis as far as I know. | |
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Wavelet and Filter Banks by G. Strang and T. Nyguen. |
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| This book explains the idea of filter bank algorithm with the connection of wavelet in favor of engineering . The authors give us easy and elementary technique for computatuon | |
| Wavelet and Subband Coding Theory by M.Vetterli and Kovacevic | |
| Wavelet is generated by filter banks using subband coding technique in this book . This book is necessary for the study of wavelet. It also describes an application of wavelet to signal processing and image processing. | |
| An Introductiopn to K-Theory for C^{/sp*} Algebras by Rordam,Larsen and Laustsen | |
| Well written Text for K thoery of C^{/sp*} algebras But it doesn't mention K-homology. For this, Nigel Higson and John Roe's Analytic K-Homology is Recommended. | |