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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Introduction to Operator Theory in Riesz Spaces (Paperback, Softcover reprint of the original 1st ed. 1997)
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Introduction to Operator Theory in Riesz Spaces (Paperback, Softcover reprint of the original 1st ed. 1997)
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Since the beginning of the thirties a considerable number of books
on func tional analysis has been published. Among the first ones
were those by M. H. Stone on Hilbert spaces and by S. Banach on
linear operators, both from 1932. The amount of material in the
field of functional analysis (in cluding operator theory) has grown
to such an extent that it has become impossible now to include all
of it in one book. This holds even more for text books. Therefore,
authors of textbooks usually restrict themselves to normed spaces
(or even to Hilbert space exclusively) and linear operators in
these spaces. In more advanced texts Banach algebras and (or)
topological vector spaces are sometimes included. It is only
rarely, however, that the notion of order (partial order) is
explicitly mentioned (even in more advanced exposi tions), although
order structures occur in a natural manner in many examples (spaces
of real continuous functions or spaces of measurable function ).
This situation is somewhat surprising since there exist important
and illuminating results for partially ordered vector spaces, in .
particular for the case that the space is lattice ordered. Lattice
ordered vector spaces are called vector lattices or Riesz spaces.
The first results go back to F. Riesz (1929 and 1936), L. Kan
torovitch (1935) and H. Freudenthal (1936)."
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