H.H. Schaefer Banach Lattices and Positive Operators 9783642659720

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Автор: H.H. Schaefer
Название: Banach Lattices and Positive Operators
ISBN: 9783642659720
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

ISBN-10: 3642659721
Обложка/Формат: Paperback
Страницы: 378
Вес: 0.63 кг.
Дата издания: 15.11.2011
Серия: Grundlehren der mathematischen Wissenschaften
Язык: English
Размер: 244 x 170 x 21
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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 Banachs 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.

Banach Lattices and Positive Operators, H.H. Schaefer