Representation and extension of orthoregular bilinear operators

Representation and extension of orthoregular bilinear operators

Автор: Gerard Buskes , Kusraev Anatoly G.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 1 т.9, 2007 года.

Бесплатный доступ

In this paper we study some important structural properties of orthosymmetric bilinear operators using the concept of the square of an Archimedean vector lattice. Some new results on extension and analytical representation of such operators are presented.

Короткий адрес: https://sciup.org/14318201

IDR: 14318201

Список литературы Representation and extension of orthoregular bilinear operators

  • Abramovich Yu. A. Multiplicative representation of disjointness preserving operators//Indag. Math. N. S.-1983.-V. 45, № 3.-P. 265-279.
  • Aliprantis C. D., Burkinshaw O. Positive Operators.-New York: Acad. press, 1985.-xvi+375 p.
  • Azouzi Y., Boulabiar K., Buskes G. The de Schipper formula and squares of Riesz spaces//Indag. Math. N. S.-2006.-V. 17, № 4.-P. 265-279.
  • Bernau S. J., Huijsmans C. B. Almost f-algebras and d-algebras//Math. Proc. London Phil. Soc.-1990.-V. 107.-P. 287-308.
  • Boulabiar K. Some aspects of Riesz multimorphisms//Indag. Math. N. S.-2002.-V. 13, № 4.-P. 419-432.
  • Boulabiar K, Buskes G. Vector lattice powers: f-algebras and functional calculus//Comm. Algebra.-2006.-V. 34, № 4.-P. 1435-1442.
  • Boulabiar K., Buskes G., Page R. On some properties of bilinear maps of order bounded variation//Positivity.-2005.-V. 9, № 3.-P. 401-414.
  • Boulabiar K., Tuomi M. A. Lattice bimorphisms on f-algebras//Ordered Algebraic Structures/Ed. J. Martinez.-Dordrecht: Kluwer, 2002.-P. 179-188.
  • Bu Q., Buskes G., Kusraev A. G. Bilinear maps on product of vector lattices, to appear.
  • Buskes G., van Rooij A. Hahn-Banach for Riesz homomorphisms//Indag. Math.-1993.-V. 51.-P. 25-34.
  • Buskes G., van Rooij A. Almost f-algebras: structure and Dedekind completion//Positivity.-2000.-V. 4.-P. 233-243.
  • Buskes G., van Rooij A. Almost f-algebras: commutativity and the Cauchy-Schwarz in equality//Positivity.-2000.-V. 4.-P. 227-231.
  • Buskes G., van Rooij A. Squares of Riesz spaces//Rocky Mountain J. Math.-2001.-V. 31, № 1.-P. 45-56.
  • Buskes G., van Rooij A. Bounded variation and tensor products of Banach lattices//Positivity.-2003.-V. 7, № 1/2.-P. 47-59.
  • Dragomir S. S. A Survey on Cauchy-Buniakowsky-Schwartz Type Discrete Inequalities.-Victoria University, RGMIA Monographs, 2000.-288 p.
  • Fremlin D. H. Tensor product of Archimedean vector lattices//Amer. J. Math.-1972.-V. 94.-P. 777-798.
  • Gaans O. W. The Riesz part of a positive bilinear form//Circumspice.-Nijmegen, Katholieke Universiteit Nijmegen, 2001.-P. 19-30.
  • Grobler J. J., Labushagne C. The tensor product of Archimedean ordered vector spaces//Math. Proc. Cambridge Philos. Soc.-1988.-V. 104, № 2.-P. 331-345.
  • Gutman A. E. Banach bundles in the theory of lattice-normed spaces//Linear Operators Compatible with Order.-Novosibirsk: Sobolev Institute Press, 1995.-P. 63-211.-In Russian.
  • Gutman A. E. Disjointness preserving operators//Vector Lattices and Integral Operators/Ed. S. S. Kutateladze.-Dordrecht etc.: Kluwer, 1996.-P. 361-454.
  • Huijsmans C. B., de Pagter B. Averaging operators and positive contractive projections//J. Math. Anal. and Appl.-1986.-V. 107.-P. 163-184.
  • Kusraev A. G. On a Property of the Base of the K-space of Regular Operators and Some of Its Applications.-Novosibirsk, Sobolev Inst. of Math, 1977.-17 p.-In Russian.
  • Kusraev A. G. Dominated Operators.-Dordrecht: Kluwer, 2000.-446 p.
  • Kusraev A. G. On the representation of orthosymmetric bilinear operators in vector lattices//Vladikavkaz Math. J.-2005.-V. 7, № 4.-P. 30-34.-In Russian.
  • Kusraev A. G. On the structure of orthosymmetric bilinear operators in vector lattices//Dokl. RAS.-2006.-V. 408, № 1.-P. 25-27.-In Russian.
  • Kusraev A. G., Shotaev G. N. Bilinear majorizable operators//Studies on Complex Analysis, Operator Theory, and Mathematical Modeling!/Ed. Yu. F. Korobe\u \i nik and A. G. Kusraev.-Vladikavkaz: Vladikavkaz Scientific Center, 2004.-P. 241-262.-In Russian.
  • Kusraev A. G., Tabuev S. N. On disjointness preserving bilinear operators//Vladikavkaz. Math. J.-2004.-V. 6, № 1.-P. 58-70.-In Russian.
  • Kusraev A. G., Tabuev S. N. On multiplicative representation of disjointness preserving bilinear operators//Sib. Math. J., to appear.-In Russian.
  • Scheffold E. FF-Banachverbandsalgebren//Math. Z.-1981.-V. 177.-P. 183-205.
Еще
Статья научная
QR-код для установки приложения SciUp Наведите камеру и скачайте бесплатное приложение SciUp