<p>In this paper, we generalize several numerical radius inequalities for bounded operators on a right quaternionic Hilbert space. Among other inequalities, we show some power inequalities for the numerical radius of a product of quaternionic bounded operator which are analogous to the classical results. To achieve this, we use the complex matrix representation of quaternionic operators. As consequence of this technique, we give some equivalence conditions for the numerical range of a right quaternionic operator to be convex, generalizing finite dimensional case.</p>

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Numerical Radius Inequalities of Quaternionic Right Linear Bounded Operators

  • Somayya Moulaharabbi,
  • Mohamed Barraa

摘要

In this paper, we generalize several numerical radius inequalities for bounded operators on a right quaternionic Hilbert space. Among other inequalities, we show some power inequalities for the numerical radius of a product of quaternionic bounded operator which are analogous to the classical results. To achieve this, we use the complex matrix representation of quaternionic operators. As consequence of this technique, we give some equivalence conditions for the numerical range of a right quaternionic operator to be convex, generalizing finite dimensional case.