A note on the Banach lattice $c_0( \ell_2^n)$, its dual and its bidual

Authors

  • M.L. Lourenço University of São Paulo, São Paulo, Brazil
  • V.C.C. Miranda University of São Paulo, São Paulo, Brazil
https://doi.org/10.15330/cmp.15.1.270-277

Keywords:

Banach lattice, Dunford-Pettis property, Gelfand-Phillips property, weak Dunford-Pettis property, weak Grothendieck property, positive Grothendieck property, strong Gelfand-Phillips property
Published online: 2023-06-30

Abstract

The main purpose of this paper is to study some geometric and topological properties of $c_0$-sum of the finite dimensional Banach lattice $\ell_2^n$, its dual and its bidual. Among other results, we show that the Banach lattice $c_0(\ell_2^n)$ has the strong Gelfand-Philips property, but does not have the positive Grothendieck property. We also prove that the closed unit ball of $l_{\infty}(\ell_2^n)$ is an almost limited set.

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How to Cite
(1)
Lourenço, M.; Miranda, V. A Note on the Banach Lattice $c_0( \ell_2^n)$, Its Dual and Its Bidual. Carpathian Math. Publ. 2023, 15, 270-277.