This self-contained reference/text presents a thorough account of
the theory of real function algebras. Employing the intrinsic
approach, avoiding the complexification technique, and generalizing
the theory of complex function algebras, this single-source volume
includes: an introduction to real Banach algebras; various
generalizations of the Stone-Weierstrass theorem; Gleason parts;
Choquet and Shilov boundaries; isometries of real function
algebras; extensive references; and a detailed bibliography.;Real
Function Algebras offers results of independent interest such as:
topological conditions for the commutativity of a real or complex
Banach algebra; Ransford's short elementary proof of the
Bishop-Stone-Weierstrass theorem; the implication of the
analyticity or antianalyticity of f from the harmonicity of Re f,
Re f(2), Re f(3), and Re f(4); and the positivity of the real part
of a linear functional on a subspace of C(X).;With over 600 display
equations, this reference is for mathematical analysts; pure,
applied, and industrial mathematicians; and theoretical physicists;
and a text for courses in Banach algebras and function algebras.
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