From the reviews of the second edition:

Some praise for the previous edition:

“I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands quite alone....” (John R. Taylor, Professor of Physics and Presidential Teaching Scholar, University of Colorado at Boulder)

"This is an excellent textbook for graduate students and young researchers in mathematics and theoretical physics. … It is a course from the basics in functional analysis to bounded and unbounded operators, including spectral theory and operator algebras. The exposition is comprehensive, but self-contained." (Michael Demuth, Zentralblatt MATH, Vol. 1163, 2009)

“As the title declares, the text presents a comprehensive presentation of linear spaces and their transformations. … this second edition contains two additional chapters on quantum treatments of waveguides and graphs. … The book considered is, no doubt, written for physicists and useful for them. … A valuable feature of this book is the extensive background material and discussions collected into separate sections. … The book does what it promises and does it well.” (Stig Stenholm, Contemporary Physics, January, 2010)