UPC: 9783642659720 | Grundlehren Der Mathematischen Wissenschaften: Banach Lattices and Positive Operators (Paperback)

UPC lookup results for: 9783642659720 | Grundlehren Der Mathematischen Wissenschaften: Banach Lattices and Positive Operators (Paperback)

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.