Order bounded orthosymmetric bilinear operator

Elmiloud Chil

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 4, page 873-880
  • ISSN: 0011-4642

Abstract

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It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator b : E × E → F where E and F are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost f -algebras.

How to cite

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Chil, Elmiloud. "Order bounded orthosymmetric bilinear operator." Czechoslovak Mathematical Journal 61.4 (2011): 873-880. <http://eudml.org/doc/196787>.

@article{Chil2011,
abstract = {It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator $b\colon E\times E\rightarrow F$ where $E$ and $F$ are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost $f$-algebras.},
author = {Chil, Elmiloud},
journal = {Czechoslovak Mathematical Journal},
keywords = {vector lattice; positive bilinear operator; orthosymmetric bilinear operator; lattice bimorphism; vector lattice; positive bilinear operator; orthosymmetric bilinear operator; lattice bimorphism},
language = {eng},
number = {4},
pages = {873-880},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Order bounded orthosymmetric bilinear operator},
url = {http://eudml.org/doc/196787},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Chil, Elmiloud
TI - Order bounded orthosymmetric bilinear operator
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 873
EP - 880
AB - It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator $b\colon E\times E\rightarrow F$ where $E$ and $F$ are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost $f$-algebras.
LA - eng
KW - vector lattice; positive bilinear operator; orthosymmetric bilinear operator; lattice bimorphism; vector lattice; positive bilinear operator; orthosymmetric bilinear operator; lattice bimorphism
UR - http://eudml.org/doc/196787
ER -

References

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  1. Aliprantis, C. D., Burkinshaw, O., Positive Operators, Springer Berlin (2006). (2006) Zbl1098.47001MR2262133
  2. Basly, M., Triki, A., FF-algèbres Archimédiennes réticulées, University of Tunis, Preprint (1988). (1988) MR0964828
  3. Bernau, S. J., Huijsmans, C. B., 10.1017/S0305004100068560, Math. Proc. Camb. Philos. Soc. 107 (1990), 287-308. (1990) Zbl0707.06009MR1027782DOI10.1017/S0305004100068560
  4. Bigard, A., Keimel, K., Wolfenstein, S., Groupes et Anneaux Réticulés. Lecture Notes in Mathematics Vol. 608, Springer Berlin-Heidelberg-New York (1977). (1977) MR0552653
  5. Birkhoff, G., Pierce, R. S., Lattice-ordered rings, Anais Acad. Brasil. Ci. 28 (1956), 41-69. (1956) Zbl0070.26602MR0080099
  6. Bu, Q., Buskes, G., Kusraev, A. G., Bilinear Maps on Product of Vector Lattices: A Survey. Positivity. Trends in Mathematics, Birkhäuser Basel (2007), 97-126. (2007) MR2382216
  7. Buskes, G., Pagter, B. de, Rooij, A. van, 10.1016/0019-3577(91)90028-6, Indag. Math. New Ser. 4 (1991), 423-436. (1991) MR1149692DOI10.1016/0019-3577(91)90028-6
  8. Buskes, G., Kusraev, A. G., Representation and extension of orthoregular bilinear operators, Vladikavkaz. Math. Zh. 9 (2007), 16-29. (2007) MR2434620
  9. Buskes, G., Rooij, A. van, 10.1017/S0305004100077902, Math. Proc. Camb. Philos. Soc. 105 (1989), 523-536. (1989) MR0985689DOI10.1017/S0305004100077902
  10. Buskes, G., Rooij, A. van, 10.1023/A:1009826510957, Positivity 4 (2000), 227-231. (2000) MR1797125DOI10.1023/A:1009826510957
  11. Buskes, G., Rooij, A. van, 10.1216/rmjm/1008959667, Rocky Mt. J. Math. 31 (2001), 45-56. (2001) MR1821367DOI10.1216/rmjm/1008959667
  12. Buskes, G., Rooij, A. van, 10.1023/A:1025898718431, Positivity 7 (2003), 47-59. (2003) MR2028366DOI10.1023/A:1025898718431
  13. Grobler, J. J., Labuschagne, C. C. A., 10.1017/S0305004100065506, Math. Proc. Camb. Philos. Soc. 104 (1988), 331-345. (1988) Zbl0663.46006MR0948918DOI10.1017/S0305004100065506
  14. Huijsmans, C. B., Pagter, B. de, 10.1112/plms/s3-48.1.161, Proc. Lond. Math. Soc. III. Ser. 48 (1984), 161-174. (1984) Zbl0534.46010MR0721777DOI10.1112/plms/s3-48.1.161
  15. Luxemburg, W. A. J., Zaanen, A. C., Riesz spaces I, North-Holland Mathematical Library Amsterdam-London (1971). (1971) MR0511676
  16. Nakano, H., Product spaces of semi-ordered linear spaces, J. Fac. Sci., Hakkaidô Univ. Ser. I. 12 (1953), 163-210. (1953) Zbl0051.33901MR0062961
  17. Zaanen, A. C., Riesz spaces II, North-Holland Mathematical Library Amsterdam-New York-Oxford (1983). (1983) Zbl0519.46001MR0704021

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