An Operator Inequality Which Implies Paranormality

An Operator Extension of Bohr's inequality

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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Pinched exponential volume growth implies an infinite dimensional isoperimetric inequality

Let G be a graph which satisfies c−1 ar ≤ |B(v, r)| ≤ c ar, for some constants c, a > 1, every vertex v and every radius r. We prove that this implies the isoperimetric inequality |∂A| ≥ C|A|/ log(2 + |A|) for some constant C = C(a, c) and every finite set of vertices A. A graph G = ( V (G), E(G) ) has pinched growth f(r) if there are two constants 0 < c < C < ∞ so that every ball B(v, r) of ra...