
Banach Lattices and Positive Operators
H.H. Schaefer(Author)
Springer (Publisher)
Published on 15. November 2011
Book
Paperback/Softback
XII, 378 pages
978-3-642-65972-0 (ISBN)
Description
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.
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1974
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XII, 378 p.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 22 mm
Weight
681 gr
ISBN-13
978-3-642-65972-0 (9783642659720)
DOI
10.1007/978-3-642-65970-6
Schweitzer Classification
Other editions
Additional editions
H.H. Schaefer
Banach Lattices and Positive Operators
Book
12/1974
Springer
€85.55
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Content
I. Positive Matrices.- Notes.- Exercises.- II. Banach Lattices.- Notes.- Exercises.- III. Ideal and Operator Theory.- Notes.- Exercises.- IV. Lattices of Operators.- Notes.- Exercises.- V. Applications.- Notes.- Exercises.- Index of Symbols.