Linear Operators and Their Spectra

This book was published by Cambridge University Press in April 2007. Further information may be found at

the CUP web site.

The following is an extract from the preface.

"It is frequently said that over the last few decades there has been a decisive shift in mathematics from the linear to the non-linear. Even if this is the case it is easy to justify writing a book on the theory of linear operators. The range of applications of the subject continues to grow rapidly, and young researchers need to have an accessible account of its main lines of development, together with references to further sources for more detailed reading.

Probability theory and quantum theory are two absolutely fundamental fields of science. In terms of their technological impact they have been far more important than Einstein's relativity theory. Both are entirely linear. In the first case this is in the nature of the subject. Many sustained attempts have been made to introduce non-linearities into quantum theory, but none has yet been successful, while the linear theory has gone from triumph to triumph. Nobody can predict what the future will hold, but it seems likely that quantum theory will be used for a long time yet, even if a non-linear successor is found."

The copyright of my book "Linear Operators and Their Spectra" belongs to Cambridge University Press, but the author has permission to put a copy on the web, in the hope that some readers may be encouraged to buy the paper version.

Online version of "Linear Operators and Their Spectra"

Supplement 32, updated 8 November 2012

Review by N P Landsman, published in Mathematical Intelligencer, vol. 31

See MR2359869 (2008k:47001) for the Mathematical Reviews item on this book.