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<p>This paper is devoted to the study of the concept of normality in real AW*-algebras. The authors examine whether normality is preserved when passing from a complex AW*-algebra to its real part and prove that all real AW*-factors are normal. Conditions are established under which a real AW*-algebra is normal, in particular, when its center is locally <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-finite. The obtained results serve as real analogs of known theorems on normality in AW*-algebras and contribute to the development of operator algebra theory in the real setting.</p>

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NORMALITY IN REAL AW*-ALGEBRAS

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • S. A. Chepukhalin,
  • A. A. Rakhimov

摘要

This paper is devoted to the study of the concept of normality in real AW*-algebras. The authors examine whether normality is preserved when passing from a complex AW*-algebra to its real part and prove that all real AW*-factors are normal. Conditions are established under which a real AW*-algebra is normal, in particular, when its center is locally \(\sigma \) σ -finite. The obtained results serve as real analogs of known theorems on normality in AW*-algebras and contribute to the development of operator algebra theory in the real setting.