<p>Let <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({\mathcal {A}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">A</mi> </math></EquationSource> </InlineEquation> be an <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-algebra containing a non-trivial projection with unit <i>I</i>. In this paper, we study the characterization of nonlinear mixed skew Jordan triple <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>- derivations on <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-algebras. In particular, we can also apply our result in von-Neumann algebras, standard operator algebras and prime <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-algebras. Moreover, by an example we illustrate that the given maps are true in case of non-trivial structures that exist with these algebras.</p>

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Characterization of nonlinear mixed skew Jordan triple \(*\)-derivations on \(*\)-algebras

  • Nadeem ur Rehman,
  • Shaheen Khan,
  • Junaid Nisar

摘要

Let \({\mathcal {A}}\) A be an \(*\) -algebra containing a non-trivial projection with unit I. In this paper, we study the characterization of nonlinear mixed skew Jordan triple \(*\) - derivations on \(*\) -algebras. In particular, we can also apply our result in von-Neumann algebras, standard operator algebras and prime \(*\) -algebras. Moreover, by an example we illustrate that the given maps are true in case of non-trivial structures that exist with these algebras.