An operator inequality and its consequences

An Operator Extension of Bohr's inequality

Jensen’s Operator Inequality and Its Converses

where φ : A → B(H) is a unital completely positive linear map from a C-algebra A to linear operators on a Hilbert space H, and x is a self-adjoint element in A with spectrum in I. Subsequently M. D. Choi [3] noted that it is enough to assume that φ is unital and positive. In fact, the restriction of φ to the commutative C-algebra generated by x is automatically completely positive by a theorem ...

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's inequality

an operator extension of bohr&apos;s inequality

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