Kantorovich's principle in action: AW*-modules and injective Banach lattices

Kantorovich's principle in action: AW*-modules and injective Banach lattices

Автор: Kusraev Anatoly G.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 1 т.14, 2012 года.

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Making use of Boolean valued representation it is proved that Kaplansky--Hilbert lattices and injective Banach lattices may be produced from each other by means of the convexification procedure. The relationship between the Kantorovich's heuristic principle and the Boolean value transfer principle is also discussed.

Kantorovich's principle, kaplansly--hilbert module, injective banach lattice, boolean valued analysis, boolean valued representation, maharam operator, square of a vector lattice, convexification.

Короткий адрес: https://sciup.org/14318373

IDR: 14318373

Список литературы Kantorovich's principle in action: AW*-modules and injective Banach lattices

  • Abramovich Y. A., Aliprantis C. D. An Invitation to Operator Theory.-Providence (R.I.): Amer. Math. Soc, 2002.-iv+530 p.
  • Arendt W. Factorization by lattice homomorphisms~/\!/Math. Z.-1984.-Vol. 185, № 4.-P. 567-571.
  • Bell J. L. Boolean-Valued Models and Independence Proofs in Set Theory.-New York etc.: Clarendon Press, 1985.-xx+165 pp.
  • Behrends E. M-Structure and Banach-Stone Theorem.-Berlin etc.: Springer, 1979.-(Lecture Notes in Math., 736.)
  • Buskes G. Separably-injective Banach lattices are injective//Proc. Roy. Irish Acad. Sect.-1985.-Vol. A85, № 2.-P. 185-186.
  • Buskes G., Kusraev A. G. Representation and extension of orthoregular bilinear operators//Vladikavkaz Math. J.-2007.-Vol. 9, № 1.-P. 16-29.
  • Buskes G., de Pagter B., van Rooij A. Functional calculus in Riesz spaces//Indag. Math. (N. S.).-1991.-Vol. 4, № 2.-P. 423-436.
  • Buskes G., van Rooij A. Squares of Riesz spaces//Rocky Mountain J. Math.-2001.-Vol. 31, №1.-P. 45-56.
  • Cartwright D. I. Extension of positive operators between Banach lattices//Memoirs Amer. Math. Soc.-1975.-Vol. 164.-P. 1-48.
  • Gordon E. I. Real numbers in Boolean-valued models of set theory and K-spaces//Dokl. Akad. Nauk SSSR.-1977.-Vol. 237, № 4.-P. 773-775.
  • Gordon E. I. K-spaces in Boolean-valued models of set theory//Dokl. Akad. Nauk SSSR.-1981.-Vol. 258, № 4.-P. 777-780.
  • Gordon E. I. To the theorems of identity preservation in K-spaces//Sibirsk. Mat. Zh.-1982.-Vol. 23, № 5.-P. 55-65.
  • Harmand P., Werner D., Wener W. M-Ideals in Banach Spaces and Banach Algebras.-Berlin etc.: Springer, 1993.-viii+384 p.-(Lecture Notes in Math, 1547).
  • Haydon R. Injective Banach lattices//Math. Z.-1977.-Vol. 156.-P. 19-47.
  • Ivanov V. V. Banach Topologies and Kolmogorov's Problem.-Novosibirsk: Sobolev Inst. Math., 2011.-16 p.-(Preprint \No~257).-[in Russian].
  • Kantorovich L. V. On semiordered linear spaces and their applications to the theory of linear operations//Dokl. Akad. Nauk SSSR.-1935.-Vol. 4, № 1-2.-P. 11-14.
  • Kantorovich L. V., Vulikh B. Z., Pinsker A. G. Functional Analysis in Semiordered Spaces.-Moscow-Leningrad: Gostekhizdat, 1950.-548 p.-[in Russian].
  • Kaplansky I. Modules over operator algebras//Amer. J. Math.-1953.-Vol.75, № 4.-P. 839-858.
  • Kusraev A. G. Dominated Operators.-Dordrecht: Kluwer, 2000.-446 p.
  • Kusraev A. G. A Radon-Nikodym type theorem for orthosymmetric bilinear operators//Positivity.-2010.-Vol. 14, № 2.-P. 225-238.
  • Kusraev A. G. Boolean Valued Analysis Approach to Injective Banach Lattices.-Vladikavkaz: Southern Math. Inst. VSC RAS, 2011.-28 p.-(Preprint №1).
  • Kusraev A. G., Kutateladze S. S. Boolean Valued Analysis.-Novosibirsk: Nauka, 1999.-383 p.-[in Russian]; (English transl.: Dordrecht: Kluwer, 1999.)
  • Kusraev A. G., Kutateladze S. S. Introduction to Boolean Valued Analysis.-Moscow: Nauka, 2005.-526 p.-[in Russian].
  • Kutateladze S. S. Mathematics and Economics in the Legacy of Leonid Kantorovich//This issue.-P. 7-21.
  • Lindenstrauss J., Tzafriri L. Classical Banach Spaces. Vol. 2. Function Spaces.-Berlin etc.: Springer-Verlag, 1979.-x+243 p.
  • Lotz H. P. Extensions and liftings of positive linear mappings on Banach lattices//Trans. Amer. Math. Soc.-1975.-Vol. 211.-P. 85-100.
  • Meyer-Nieberg P. Banach Lattices.-Berlin etc.: Springer-Verlag, 1991.-xvi+395 p.
  • Ozawa M. Boolean valued interpretation of Hilbert space theory//J. Math. Soc. Japan.-1983.-Vol. 35, № 4.-P. 609-627.
  • Ozawa M. A classification of type I AW*-algebras and Boolean valued analysis//J. Math. Soc. Japan.-1984.-Vol. 36, № 4.-P. 589-608.
  • Ozawa M. Boolean valued interpretation of Banach space theory and module structure of von Neumann algebras//Nagoya Math. J.-1990.-Vol. 117.-P. 1-36.
  • Szulga J. (p,r)-convex functions on vector lattices//Proc. Edinburg Math. Soc.-1994.-Vol. 37, № 2.-P. 207-226.
  • Takeuti G. Two Applications of Logic to Mathematics.-Princeton: Princeton Univ. Press, 1978.-viii+137 p.
  • Takeuti G. Boolean valued analysis//Applications of Sheaves (Proc. Res. Sympos. Appl. Sheaf Theory to Logic, Algebra and Anal., Univ. Durham, Durham, 1977).-Berlin etc.: Springer-Verlag, 1979.-P. 714-731.-(Lecture Notes in Math., 753.)
  • Takeuti G. Boolean completion and m-convergence//Categorical Aspects of Topology and Analysis (Ottawa, Ont., 1980).-Berlin etc.: Springer-Verlag, 1982.-P. 333-350.-(Lecture Notes in Math., 915.)
  • Vulikh B. Z. Introduction to the Theory of Partially Ordered Spaces.-Moscow: Fizmatgiz, 1961.-407 p.-[in Russian].
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