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eBook Introduction to Operator Theory in Riesz Spaces download

by Adriaan C. Zaanen

eBook Introduction to Operator Theory in Riesz Spaces download ISBN: 3540619895
Author: Adriaan C. Zaanen
Publisher: Springer; 1 edition (January 15, 1997)
Language: English
Pages: 312
ePub: 1496 kb
Fb2: 1374 kb
Rating: 4.4
Other formats: lrf docx lit mbr
Category: Math Sciences
Subcategory: Mathematics

The book deals with the structure of vector lattices, . Riesz spaces, and Banach lattices, as well as with operators in these spaces. The methods used are kept as simple as possible. Almost no prior knowledge of functional analysis is required.

The book deals with the structure of vector lattices, . For most applications some familiarity with the oridinary Lebesgue integral is already sufficient. In this respect the book differs from other books on the subject. In most books on functional analysis (even excellent ones) Riesz spaces, Banach lattices and positive operators are mentioned only briefly, or even not at all. The present book shows how.

The book deals with the structure of vector lattices, . For most applications some familiarity with the ordinary Lebesgue integral is already sufficient.

Since the beginning of the thirties a considerable number of books on func tional analysis has been published.

The first results go back to F. Riesz (1929 and 1936), L. Kan torovitch (1935) and H. Freudenthal (1936). Since the beginning of the thirties a considerable number of books on func tional analysis has been published. Among the first ones were those by M. H. Stone on Hilbert spaces and by S. Banach on linear operators, both from 1932. The amount of material in the field of functional analysis (in cluding operator theory) has grown to such an extent that it has become impossible now to include all of it in one book. This holds even more for text books.

Seems like a reasonable text as an introduction to Riesz spaces. Also, the short list of other books on Riesz spaces included at the back of the book is very short and seems not to include any in-depth resources for the new results. The book jacket advertises that it contains new developments in the field, but the structure of the book makes it difficult to determine where the new results are located. One person found this helpful.

Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper Sur la décomposition . Zaanen, Adriaan C. (1996), Introduction to Operator Theory in Riesz spaces, Springer, ISBN 3-540-61989-5.

Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper Sur la décomposition des opérations fonctionelles linéaires. Riesz spaces have wide ranging applications. They are important in measure theory, in that important results are special cases of results for Riesz Spaces. the Radon–Nikodym theorem follows as a special case of the Freudenthal spectral theorem. Riesz spaces have also seen application in mathematical economics through the work of Greek-American economist and mathematician Charalambos D. Aliprantis.

Автор: Adriaan C. Zaanen Название: Introduction to Operator Theory in Riesz Spaces Издательство: Springer .

Author: Adriaan C. Zaanen. Locally solid Riesz spaces. Introduction to Operator Space Theory. Introduction to linear operator theory. Topological Riesz Spaces and Measure Theory.

Assembled Product Dimensions (L x W x H). 1 x . 4 x . 9 Inches.

Finding books BookSee BookSee - Download books for free. Introduction to Operator Theory in Riesz Spaces. 5. 2 Mb. Riesz Spaces, II (North-Holland Mathematical Library) (v. 2). A. C.

Since the beginning of the thirties a considerable number of books on func­ tional analysis has been published. Among the first ones were those by M. H. Stone on Hilbert spaces and by S. Banach on linear operators, both from 1932. The amount of material in the field of functional analysis (in­ cluding operator theory) has grown to such an extent that it has become impossible now to include all of it in one book. This holds even more for text­ books. Therefore, authors of textbooks usually restrict themselves to normed spaces (or even to Hilbert space exclusively) and linear operators in these spaces. In more advanced texts Banach algebras and (or) topological vector spaces are sometimes included. It is only rarely, however, that the notion of order (partial order) is explicitly mentioned (even in more advanced exposi­ tions), although order structures occur in a natural manner in many examples (spaces of real continuous functions or spaces of measurable function~). This situation is somewhat surprising since there exist important and illuminating results for partially ordered vector spaces, in . particular for the case that the space is lattice ordered. Lattice ordered vector spaces are called vector lattices or Riesz spaces. The first results go back to F. Riesz (1929 and 1936), L. Kan­ torovitch (1935) and H. Freudenthal (1936).