A proof via operator means of an order preserving inequality

An Operator Extension of Bohr's inequality

an operator extension of bohr's inequality

Second Order Arithmetic Means in Operator Ideals

We settle in the negative the question arising from [3] on whether equality of the second order arithmetic means of two principal ideals implies equality of their first order arithmetic means (second order equality cancellation) and we provide fairly broad sufficient conditions on one of the principal ideals for this implication to always hold true. We present also sufficient conditions for sec...

An Operator Inequality Related to Jensen’s Inequality

For bounded non-negative operators A and B, Furuta showed 0 ≤ A ≤ B implies A r 2BA r 2 ≤ (A r 2BA r 2 ) s+r t+r (0 ≤ r, 0 ≤ s ≤ t). We will extend this as follows: 0 ≤ A ≤ B ! λ C (0 < λ < 1) implies A r 2 (λB + (1− λ)C)A r 2 ≤ {A r 2 (λB + (1 − λ)C)A r 2 } s+r t+r , where B ! λ C is a harmonic mean of B and C. The idea of the proof comes from Jensen’s inequality for an operator convex functio...

an operator extension of bohr&apos;s inequality

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