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<p>Let <i>A</i> be a commutative and unitary <i>f</i>-algebra with bounded inversion, and let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(A^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>A</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation> be the subalgebra of bounded elements. This paper deals with subalgebras of <i>A</i> containing <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(A^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>A</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>. We prove that these intermediate algebras in <i>A</i> are also <i>f</i>-algebras with bounded inversion and we extend to them most of the basic results about intermediate algebras between <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(C^*(X)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>C</mi> <mo>∗</mo> </msup> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <i>C</i>(<i>X</i>) developed by Domínguez, Gómez-Pérez, and Mulero.</p>

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Intermediate algebras in f-algebras with bounded inversion

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • J. M. Domínguez,
  • M. A. Mulero

摘要

Let A be a commutative and unitary f-algebra with bounded inversion, and let \(A^*\) A ∗ be the subalgebra of bounded elements. This paper deals with subalgebras of A containing \(A^*\) A ∗ . We prove that these intermediate algebras in A are also f-algebras with bounded inversion and we extend to them most of the basic results about intermediate algebras between \(C^*(X)\) C ∗ ( X ) and C(X) developed by Domínguez, Gómez-Pérez, and Mulero.