My Favorite Books


C* lagebras and their Automorphism Groups by G.K.Pedersen

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.
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.

Wavelet and Filter Banks by G. Strang and T. Nyguen.


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.