Theoretical analysis establishes a novel pseudo-mean for bounded linear operators on Hilbert spaces, demonstrating foundational operator inequalities.
In this paper, we introduce the pseudo-mean A◯pνB:=||BA†|νA|2 for bounded linear operators A and B on a Hilbert space H, where A has closed range and ν≥0. We establish several inequalities for this pseudo-mean and provide an illustrative example.
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Jabbarzadeh et al. (2026) studied this question.
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