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<p>In this paper we prove that for (<i>ru</i>)-complete semiprime <i>f</i>-algebras with weak order units, <i>A</i> is a Banach lattice if and only if <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Orth(A)=Stab(A)=Z(A)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mi>r</mi> <mi>t</mi> <mi>h</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>S</mi> <mi>t</mi> <mi>a</mi> <mi>b</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. This answers a natural question posed by Wickstead in [Wójtowicz, M., Wisniewska, H.: The problem of central orthomorphisms in a class of <i>F</i>-lattices. Indag. Math. New Ser. <b>26</b>(2), 393–403 (2015)]. The inspiration for this characterization arises from a rigorous study of finite elements in Archimedean vector lattices. Furthermore, by introducing a new class of orthomorphisms, termed pseudo-center, we affirmatively solve its related Wickstead problem.</p>

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Centered orthomorphisms and the Wickstead problem

  • 期刊论文

  • 发表日期：

    2026年4月4日

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  • Mohamed Ali Toumi,
  • Nedra Toumi,
  • Zied Jbeli

摘要

In this paper we prove that for (ru)-complete semiprime f-algebras with weak order units, A is a Banach lattice if and only if \(Orth(A)=Stab(A)=Z(A)\) O r t h ( A ) = S t a b ( A ) = Z ( A ) . This answers a natural question posed by Wickstead in [Wójtowicz, M., Wisniewska, H.: The problem of central orthomorphisms in a class of F-lattices. Indag. Math. New Ser. 26(2), 393–403 (2015)]. The inspiration for this characterization arises from a rigorous study of finite elements in Archimedean vector lattices. Furthermore, by introducing a new class of orthomorphisms, termed pseudo-center, we affirmatively solve its related Wickstead problem.