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This book is mainly concerned with the theory of Banach lattices
and with linear operators defined on, or with values in Banach
lattices. Moreover we will always consider more general classes of
Riesz spaces so long as this does not involve more complicated
constructions or proofs. In particular, we will not treat any
phenomena which occur only in the non-Banach lattice situation.
Riesz spaces, also called vector lattices, K-lineals, are linear
lattices which were first considered by F. Riesz, 1. Kantorovic,
and H. Freudenthal. Subse- quently other important contributions
came from the Soviet Union (L.V. Kan- torovic, A.J. Judin, A.G.
Pinsker, and B.Z. Vulikh), Japan (H. Nakano, T. Oga- sawara, and K.
Yosida), and the United States (G. Birkhoff, H.F. Bohnenblust, S.
Kakutani, and M.l\f. Stone). In the last twenty-five years the
theory rapidly increased. Important con- tributions came from the
Dutch school (W.A.J. Luxemburg, A.C. Zaanen) and the Tiibinger
school (lI.lI. Schaefer). In the middle seventies the research on
this subject was essentially influenced by the books of H.H.
Schaefer (1974) and W.A.J. Luxemburg and A.C. Zaanen (1971). More
recently other impor- tant books concerning this subject appeared,
A.C. Zaanen (1983), H.U. Schwarz (1984), and C.D. Aliprantis and O.
Burkinshaw (1985).
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