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, ...
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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). L. Kantorovic and his school first recognized the importance of studying vector lattices in connection with Banach's theory of normed vector spaces; they investigated normed vector lattices as well as order-related linear operators between such vector lattices. (Cf. Kantorovic-Vulikh-Pinsker [1950] and Vulikh [1967].) However, in the years following that early period, functional analysis and vector lattice theory began drifting more and more apart; it is my impression that "linear order theory" could not quite keep pace with the rapid development of general functional analysis and thus developed into a theory largely existing for its own sake, even though it had interesting and beautiful applications here and there.
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Add this copy of Branch Lattices & Positive Operators (Grundelhren Der to cart. $65.50, good condition, Sold by HPB-Red rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 1975 by Springer Verlag.
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Good; Hardcover; 1975, Springer Publishing; Former library copy with standard library markings; Moderate wear to covers; Library stamps to endpapers; Text pages clean & unmarked; Good binding with straight spine; Yellow cloth covers with title in black lettering; 376 pages; "Branch Lattices & Positive Operators (Grundelhren Der Mathematischen Wissenschaften), " by H. H. Schaefer.
Add this copy of Banach Lattices and Positive Operators: 215 to cart. $74.85, good condition, Sold by Stephen White Books rated 5.0 out of 5 stars, ships from Bradford, WEST YORKSHIRE, UNITED KINGDOM, published 1974 by Springer.
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