The triadjoint of an orthosymmetric bimorphism

Mohamed Ali Toumi

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 1, page 85-94
  • ISSN: 0011-4642

Abstract

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Let A and B be two Archimedean vector lattices and let ( A ' ) n ' and ( B ' ) n ' be their order continuous order biduals. If Ψ : A × A → B is a positive orthosymmetric bimorphism, then the triadjoint Ψ * * * : ( A ' ) n ' × ( A ' ) n ' → ( B ' ) n ' of Ψ is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost f -algebras.

How to cite

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Toumi, Mohamed Ali. "The triadjoint of an orthosymmetric bimorphism." Czechoslovak Mathematical Journal 60.1 (2010): 85-94. <http://eudml.org/doc/37990>.

@article{Toumi2010,
abstract = {Let $A$ and $B$ be two Archimedean vector lattices and let $( A^\{\prime \}) _n^\{\prime \}$ and $( B^\{\prime \}) _n^\{\prime \}$ be their order continuous order biduals. If $\Psi \colon A\times A\rightarrow B$ is a positive orthosymmetric bimorphism, then the triadjoint $\Psi ^\{\ast \ast \ast \}\colon ( A^\{\prime \}) _n^\{\prime \}\times ( A^\{\prime \}) _n^\{\prime \}\rightarrow ( B^\{\prime \}) _n^\{\prime \}$ of $\Psi $ is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost $f$-algebras.},
author = {Toumi, Mohamed Ali},
journal = {Czechoslovak Mathematical Journal},
keywords = {almost $f$-algebra orthosymmetric bimorphism; almost -algebra orthosymmetric bimorphism},
language = {eng},
number = {1},
pages = {85-94},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The triadjoint of an orthosymmetric bimorphism},
url = {http://eudml.org/doc/37990},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Toumi, Mohamed Ali
TI - The triadjoint of an orthosymmetric bimorphism
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 1
SP - 85
EP - 94
AB - Let $A$ and $B$ be two Archimedean vector lattices and let $( A^{\prime }) _n^{\prime }$ and $( B^{\prime }) _n^{\prime }$ be their order continuous order biduals. If $\Psi \colon A\times A\rightarrow B$ is a positive orthosymmetric bimorphism, then the triadjoint $\Psi ^{\ast \ast \ast }\colon ( A^{\prime }) _n^{\prime }\times ( A^{\prime }) _n^{\prime }\rightarrow ( B^{\prime }) _n^{\prime }$ of $\Psi $ is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost $f$-algebras.
LA - eng
KW - almost $f$-algebra orthosymmetric bimorphism; almost -algebra orthosymmetric bimorphism
UR - http://eudml.org/doc/37990
ER -

References

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