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- Alexander E. Gutman, Anatoly G. Kusraev, Semen S. Kutateladze, Anthony Wickstead
- 2007

In 1977 Anthony Wickstead raised the question of the conditions for all band preserving linear operators to be order bounded in a vector lattice. This article overviews the main ideas and results on the Wickstead problem and its variations, focusing primarily on the case of band preserving operators in a universally complete vector lattice. is the date of… (More)

- BILINEAR OPERATORS, Anatoly G. Kusraev
- 2008

The aim of this note is to present some properties of orthosymmetric bilinear operators which are well known for f -algebra multiplication but despite of their simplicity does not seem appeared in the literature. All unexplained terms can be found in [1] or [13]. All vector lattices under consideration are assumed to be Archimedean. 1. A bilinear operator b… (More)

This is an overview of the recent results of interaction of Boolean valued analysis and vector lattice theory.

- Anatoly G. Kusraev, S. N. Tabuev
- 2012

The study of Banach lattices in terms of sections of continuous Banach bundles has been started by Giertz [1, 2]. Later Gutman create the theory of ample (or complete) continuous Banach bundles [3] and measurable Banach bundles admitting lifting [4]. A portion of the Gutman’s theory was specified in the case of bundles of measurable Banach lattices by… (More)

- Anatoly G. Kusraev, Gleb Akilov
- 2011

An easy modification of the continuous functional calculus on unitary f -algebras as defined in [3] makes it possible to translate the Fenchel–Moreau duality to f -algebra setting and to produce some envelope representations results, see [8]. This machinery, often called quasilinearization (see [2, 9]), yields the validity of some classical inequalities in… (More)

- Elena K. Basaeva, Anatoly G. Kusraev, Semen S. Kutateladze
- J. Optimization Theory and Applications
- 2016

The aim of this note is to demonstrate that Kaplansky–Hilbert lattices and injective Banach lattices may be produced from each other by means of the well known convexification procedure. This is done via the Boolean valued analysis approach. The subject gives a good opportunity to discuss also the relationship between the Kantorovich’s heuristic principle… (More)

This paper is a continuation of [5]. We apply the upper envelope representation method (or the quasilinearization method) in vector lattices developed in [4, 5] to the homogeneous functional calculus of linear and bilinear operators. Explicit formulae for computing φ̂(T1, . . . , TN ) for any finite sequence of regular linear or bilinear operators T1, . . .… (More)

This is an expository talk on interaction between mathematical programming and vector lattices at the Kantorovich Memorial (St. Petersburg, January

The aim of this note is to give an algebraic characterization of those universally complete vector lattice in which all band preserving bilinear operators are symmetric. We start with recalling some definitions and auxiliary facts about bilinear operators on vector lattices. For the theory of vector lattices and positive operators we refer to the books [1]… (More)