Vector lattices-also called Riesz spaces, K-lineals, or linear lattices-were first considered by F. Riesz, L. Kantorovic, and H. Freudenthal in the middle nineteen thirties; thus their early theory dates back almost as far as the beginning...
of the systematic investigation of Banach spaces. Schools of research on vector lattices were subsequently founded in the Soviet Union (Kantorovic, Judin, Pinsker, Vulikh) and in Japan (Nakano, Ogasawara, Yosida); other important contri- butions came from the United States (G. Birkhoff, Kakutani, M. H. Stone).
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