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1. CMB 2011 (vol 54 pp. 577)
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Erratum: The Duality Problem For The Class of AM-Compact Operators On Banach Lattices It is proved that if a positive operator
$S: E \rightarrow F$ is AM-compact whenever its adjoint
$S': F' \rightarrow E'$ is AM-compact, then either the
norm of F is order continuous or $E'$ is discrete.
This note corrects an error in the proof of Theorem 2.3 of
B. Aqzzouz, R. Nouira, and L. Zraoula, The duality problem for
the class of AM-compact operators on Banach lattices. Canad. Math. Bull.
51(2008).
Categories:46A40, 46B40, 46B42 |
2. CMB 2008 (vol 51 pp. 15)
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The Duality Problem for the Class of AM-Compact Operators on Banach Lattices We prove the converse of a
theorem of Zaanen about the duality problem of
positive AM-compact operators.
Keywords:AM-compact operator, order continuous norm, discrete vector lattice Categories:46A40, 46B40, 46B42 |
3. CMB 2007 (vol 50 pp. 619)
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On the Existence of Asymptotic-$l_p$ Structures in Banach Spaces It is shown that if a Banach space is saturated with infinite
dimensional subspaces in which all ``special" $n$-tuples of
vectors are equivalent with constants independent of $n$-tuples and
of $n$, then the space contains asymptotic-$l_p$ subspaces
for some $1 \leq p \leq \infty$.
This extends a result by Figiel, Frankiewicz, Komorowski and
Ryll-Nardzewski.
Categories:46B20, 46B40, 46B03 |