عنوان

Banach Lattices and Positive Operators

(Number (ISBN

9783642659706

(Number (ISBN

9783642659720

Number

b407415

Title Proper

Banach Lattices and Positive Operators

General Material Designation

[Book]

First Statement of Responsibility

by Helmut H. Schaefer.

Place of Publication, Distribution, etc.

Berlin, Heidelberg :

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg,

Date of Publication, Distribution, etc.

1974.

Series Title

Die Grundlehren der mathematischen Wissenschaften,

Volume Designation

215

ISSN of Series

0072-7830 ;

Text of Note

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.

0

Text of Note

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.

International Standard Book Number

9783642659720

Title

Springer eBooks

Mathematics.

Schaefer, Helmut H.

SpringerLink (Online service)

Date of Transaction

20190301074500.0

Electronic name

[Book]

Y