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<p>The focus of the present article concerns the quaternionic <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {H}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">H</mi> </math></EquationSource> </InlineEquation>-joint numerical range of a 2-tuple of bounded right-<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb {H}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">H</mi> </math></EquationSource> </InlineEquation> linear operators in a right quaternionic Hilbert space. The connections between the geometric properties of the quaternionic <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathbb {H}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">H</mi> </math></EquationSource> </InlineEquation>-joint numerical and the algebraic properties of quaternionic bounded operators, along with spectral properties of the quaternionic Davis-Wielandt shell associated with a bounded right-<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathbb {H}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">H</mi> </math></EquationSource> </InlineEquation> linear operator, have been established.</p>

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QUATERNIONIC JOINT NUMERICAL RANGE OF A 2-TUPLE OF QUATERNIONIC BOUNDED RIGHT-\(\mathbb {H}\) LINEAR OPERATORS

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Ramkishan,
  • Preeti Dharmarha

摘要

The focus of the present article concerns the quaternionic \(\mathbb {H}\) H -joint numerical range of a 2-tuple of bounded right- \(\mathbb {H}\) H linear operators in a right quaternionic Hilbert space. The connections between the geometric properties of the quaternionic \(\mathbb {H}\) H -joint numerical and the algebraic properties of quaternionic bounded operators, along with spectral properties of the quaternionic Davis-Wielandt shell associated with a bounded right- \(\mathbb {H}\) H linear operator, have been established.