Inverses of Disjointness Preserving Operators
Inverses of Disjointness Preserving Operators

Author: Yuri A. Abramovich

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 178

ISBN-13: 0821813978

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This book is intended for graduate students and research mathematicians interested in operator theory, functional analysis, and vector lattices

Function Spaces
Function Spaces

Author: Henryk Hudzik

Publisher: CRC Press

Published: 2000-07-18

Total Pages: 534

ISBN-13: 1482270501

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This volume compiles research results from the fifth Function Spaces International Conference, held in Poznan, Poland. It presents key advances, modern applications and analyses of function spaces and contains two special sections recognizing the contributions and influence of Wladyslaw Orlicz and Genadil Lozanowskii.

Pre-Riesz Spaces
Pre-Riesz Spaces

Author: Anke Kalauch

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-11-19

Total Pages: 443

ISBN-13: 3110475448

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This monograph develops the theory of pre-Riesz spaces, which are the partially ordered vector spaces that embed order densely into Riesz spaces. Concepts from Riesz space theory such as disjointness, ideals, and bands are extended to pre-Riesz spaces. The analysis revolves around embedding techniques, including the Riesz completion and the functional representation. In the same spirit, norms and topologies on a pre-Riesz space and their extensions to the Riesz completion are examined. The generalized concepts are used to investigate disjointness preserving operators on pre-Riesz spaces and related notions. The monograph presents recent results as well as being an accessible introduction to the theory of partially ordered vector spaces and positive operators. Contents A primer on ordered vector spaces Embeddings, covers, and completions Seminorms on pre-Riesz spaces Disjointness, bands, and ideals in pre-Riesz spaces Operators on pre-Riesz spaces

Functional Analysis and Economic Theory
Functional Analysis and Economic Theory

Author: Yuri Abramovich

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 301

ISBN-13: 3642722229

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In July of 1996, the conference Nonlinear Analysis and its Applications in Engineering and Economics took place on the Greek island of Samos, the birthplace of Pythagoras. During this conference, a special session was held on th the occasion of the 50 birthday of the well known mathematician and math ematical economist Professor Charalambos Aliprantis, who, by his numerous friends, is usually called Roko. The story behind this nickname is not quite clear yet; it will be investigated further and will be made public prior to his th 60 birthday. (At this moment we have already found out that it has nothing to do with the famous movie Rocco and his Brothers even though Roko does have two brothers. ) Roko was born on the Greek island of Cephalonia on May 12,1946, and his elementary and secondary school education took place there. At 18 he entered the Mathematics Department at the University of Athens. Upon graduation from the University of Athens he proceeded with his graduate studies at Cal tech, where in 1973 he completed his Ph. D. degree in Mathematics under the supervision of Professor W. A. J. Luxemburg. His research career can be divided into two periods. The first one, till 1981, was devoted entirely to pure mathematics. The other one, after 1981, has been subdivided between pure mathematics and mathematical economics. The main objects of Roko's work in pure mathematics are spaces with order structure (Riesz spaces) and operators acting on them.