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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Factoring operators satisfying $ p$-estimates

Author: Stan Byrd
Journal: Trans. Amer. Math. Soc. 310 (1988), 567-582
MSC: Primary 47B55; Secondary 46B30, 47A68
MathSciNet review: 948187
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Abstract: Necessary and sufficient conditions for a positive operator to factor through a Banach lattice satisfying upper and lower estimates are presented. These conditions are then combined to give a necessary condition for a positive operator to factor through a super-reflexive Banach lattice. An example is given to show that, in spite of the name given by Beauzamy, uniformly convexifying operators need not factor through any uniformly convex lattice

References [Enhancements On Off] (What's this?)

  • [1] B. Beauzamy, Opèrateurs uniformèment convexifiants, Studia Math. 57 (1976), 103-139. MR 0430844 (55:3849)
  • [2] -, Introduction to Banach spaces and their geometry, North-Holland, Amsterdam, 1982. MR 670943 (84g:46017)
  • [3] J. L. Conroy and L. C. Moore, Local reflexivity in Banach lattices (preprint).
  • [4] W. J. Davis, T. Figiel, W. B. Johnson and A. Pelczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327. MR 0355536 (50:8010)
  • [5] M. M. Day, Normed linear spaces, 3rd ed., Springer-Verlag, New York, 1973. MR 0344849 (49:9588)
  • [6] N. Dunford and J. Schwartz, Linear operators, Part 1: General theory, Interscience, New York, 1958.
  • [7] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, 1952. MR 0046395 (13:727e)
  • [8] R. C. James, Super-reflexive spaces with bases, Pacific J. Math. 41 (1972), 409-419. MR 0308752 (46:7866)
  • [9] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. I, Sequence spaces, Springer-Verlag, New York, 1977. MR 0500056 (58:17766)
  • [10] -, Classical Banach spaces. II, Function spaces, Springer-Verlag, New York, 1979. MR 540367 (81c:46001)
  • [11] W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces, Amsterdam, North-Holland, 1971.
  • [12] A. Pelczyński, Some problems on bases in Banach and Fréchet spaces, Israel J. Math. 2 (1964), 132-138. MR 0173141 (30:3356)
  • [13] I. Singer, Bases in Banach spaces. I, Springer-Verlag, New York, 1970. MR 0298399 (45:7451)
  • [14] A. E. Taylor, Introduction to functional analysis, Wiley, New York, 1958. MR 0098966 (20:5411)
  • [15] B. Z. Vulikh, Introduction to the theory of partially ordered spaces, Wolters-Noordhoff, Groningen, 1967. MR 0224522 (37:121)

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Keywords: Banach lattice, positive operator, upper and lower estimates
Article copyright: © Copyright 1988 American Mathematical Society

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