Some results on order weakly compact operators

Belmesnaoui Aqzzouz; Jawad Hmichane

Mathematica Bohemica (2009)

  • Volume: 134, Issue: 4, page 359-367
  • ISSN: 0862-7959

Abstract

top
We establish some properties of the class of order weakly compact operators on Banach lattices. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms.

How to cite

top

Aqzzouz, Belmesnaoui, and Hmichane, Jawad. "Some results on order weakly compact operators." Mathematica Bohemica 134.4 (2009): 359-367. <http://eudml.org/doc/38098>.

@article{Aqzzouz2009,
abstract = {We establish some properties of the class of order weakly compact operators on Banach lattices. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms.},
author = {Aqzzouz, Belmesnaoui, Hmichane, Jawad},
journal = {Mathematica Bohemica},
keywords = {order weakly compact operator; order continuous norm; discrete vector lattice; order weakly compact operator; order continuous norm; discrete vector lattice},
language = {eng},
number = {4},
pages = {359-367},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some results on order weakly compact operators},
url = {http://eudml.org/doc/38098},
volume = {134},
year = {2009},
}

TY - JOUR
AU - Aqzzouz, Belmesnaoui
AU - Hmichane, Jawad
TI - Some results on order weakly compact operators
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 4
SP - 359
EP - 367
AB - We establish some properties of the class of order weakly compact operators on Banach lattices. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms.
LA - eng
KW - order weakly compact operator; order continuous norm; discrete vector lattice; order weakly compact operator; order continuous norm; discrete vector lattice
UR - http://eudml.org/doc/38098
ER -

References

top
  1. Aliprantis, C. D., Burkinshaw, O., Locally Solid Riesz Spaces, Academic Press (1978). (1978) Zbl0402.46005MR0493242
  2. Aliprantis, C. D., Burkinshaw, O., 10.1090/S0002-9939-1981-0627695-X, Proc. Amer. Math. Soc. 83 (1981), 573-578. (1981) Zbl0452.47038MR0627695DOI10.1090/S0002-9939-1981-0627695-X
  3. Aliprantis, C. D., Burkinshaw, O., 10.1090/S0002-9947-1982-0670929-1, Trans. Amer. Math. Soc. 274 (1982), 227-238. (1982) Zbl0498.47013MR0670929DOI10.1090/S0002-9947-1982-0670929-1
  4. Dodds, P. G., o-weakly compact mappings of Riesz spaces, Trans. Amer. Math. Soc. 214 (1975), 389-402. (1975) Zbl0313.46011MR0385629
  5. Groenewegen, G., van Rooij, A., 10.1007/BF01166700, Math. Z. 195 (1987), 473-480. (1987) Zbl0611.47032MR0900341DOI10.1007/BF01166700
  6. Meyer-Nieberg, P., Banach Lattices, Universitext. Springer, Berlin (1991). (1991) Zbl0743.46015MR1128093
  7. Schaefer, H. H., Banach Lattices and Positive Operators, Springer, Berlin (1974). (1974) Zbl0296.47023MR0423039
  8. Wickstead, A. W., 10.1093/qmath/32.2.239, Quart. J. Math. Oxford 32 (1981), 239-253. (1981) Zbl0431.47024MR0615198DOI10.1093/qmath/32.2.239
  9. Zaanen, A. C., Riesz Spaces II, North Holland Publishing Company (1983). (1983) Zbl0519.46001MR0704021

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.