Functional Analysis - Peter Lax - 2002
"...attractive...well suited for graduate courses...and useful for research
mathematicians." -- Mathematical Reviews, 2003a

Includes sections on the spectral resolution and spectral representation of
self adjoint operators, invariant subspaces, strongly continuous one-parameter
semigroups, the index of operators, the trace formula of Lidskii, the Fredholm
determinant, and more.
* Assumes prior knowledge of Naive set theory, linear algebra, point set
topology, basic complex variable, and real variables.
* Includes an appendix on the Riesz representation theorem.


Methods of Mathematical Physics Vol.1 Functional Analysis - Reed - Simon - 1981

This book is the first of a multivolume series devoted to an exposition of
functional analysis methods in modern mathematical physics. It describes the
fundamental principles of functional analysis and is essentially self-contained,
although there are occasional references to later volumes. We have included
a few applications when we thought that they would provide motivation for the
reader. Later volumes describe various advanced topics in functional analysis
and give numerous applications in classical physics, modern physics, and partial
differential equations.

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