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<p>Let <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {B}_s(\mathcal {H})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">B</mi> <mi>s</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">H</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> be the real linear space of all self-adjoint operators on a complex Hilbert space <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal {H}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">H</mi> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\dim \mathcal {H} \ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>dim</mo> <mi mathvariant="script">H</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. We characterize all continuous bijections on <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\mathcal {B}_s(\mathcal {H})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">B</mi> <mi>s</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">H</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> preserving operator pairs whose pencils are nonzero projection multipliers in both directions.</p>

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Maps on \(B_s(\mathcal {H})\) preserving operator pairs whose pencils are nonzero projection multipliers

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Jingxuan Li,
  • Guoxing Ji

摘要

Let \(\mathcal {B}_s(\mathcal {H})\) B s ( H ) be the real linear space of all self-adjoint operators on a complex Hilbert space \(\mathcal {H}\) H with \(\dim \mathcal {H} \ge 3\) dim H ≥ 3 . We characterize all continuous bijections on \(\mathcal {B}_s(\mathcal {H})\) B s ( H ) preserving operator pairs whose pencils are nonzero projection multipliers in both directions.