Atomicity in injective banach lattices

Автор: Kusraev Anatoly Georgievich

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 3 т.17, 2015 года.

Бесплатный доступ

This note is aimed to examine a Boolean valued interpretation of the concept of atomic Banach lattice and to give a complete description of the corresponding class of injective Banach lattices.

Injective banach lattice, atomic banach lattice, boolean valued representation, classification

Короткий адрес: https://sciup.org/14318508

IDR: 14318508

Список литературы Atomicity in injective banach lattices

  • Kusraev A. G. Boolean valued analysis and injective Banach lattices//Dokl. RAS.-2012.-Vol. 444, № 2.-P. 143-145.
  • Kusraev A. G. Classification of injective Banach lattices//Dokl. RAS.-2013.-Vol. 453, № 1.-P. 12-16.
  • Kusraev A. G. and Kutateladze S. S. Boolean Valued Analysis: Selected Topics.-Vladikavkaz: Vladikavkaz Scientific Center Press, 2014.-iv+400 p.-(Trends in Science. The South of Russia).
  • Aliprantis C. D. and Burkinshaw O. Positive Operators.-London etc.: Acad. Press Inc., 1985.-xvi+367 p.
  • Meyer-Nieberg P. Banach Lattices.-Berlin etc.: Springer, 1991.-xvi+395 p.
  • Lotz H. P. Extensions and liftings of positive linear mappings on Banach lattices//Trans. Amer. Math. Soc.-1975.-Vol. 211.-P. 85-100.
  • Cartwright D. I. Extension of positive operators between Banach lattices//Memoirs Amer. Math. Soc.-1975.-164 p.
  • Haydon R. Injective Banach lattices//Math. Z.-1974.-Vol. 156.-P. 19-47.
  • Kusraev A. G. A Boolean transfer principle for injective Banach lattices//Sib. Mat. Zh.-2015.-Vol. 56, № 5.-.
  • Kusraev A. G. and Kutateladze S. S. Introduction to Boolean Valued Analysis.-M.: Nauka, 2005.-526 p.-.
  • 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.
  • Kusraev A. G. Dominated Operators.-М.: Nauka, 2003.-619 p.-.
  • Luxemburg W. A. J. and Zaanen A. C. Riesz Spaces. Vol. 1.-Amsterdam and London: North-Holland, 1971.-514 p.
Еще
Статья научная