On Cauchy-Schwarz type inequalities and applications to numerical radius inequalities

2020/09/03 by Alomari, Mohammad W.
#47A12 #47A30 #47A63 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2009.01839

Abstract

In this work, a refinement of the Cauchy--Schwarz inequality in inner product space is proved. A more general refinement of the Kato's inequality or the so called mixed Schwarz inequality is established. Refinements of some famous numerical radius inequalities are also pointed out. As shown in this work, these refinements generalize and refine some recent and old results obtained in literature. Among others, it is proved that if T∈\mathscrB(\mathscrH), then ω²(T) amp;≤ (1)/(12) ‖ | T |+| T^* |‖² + (1)/(3) ω(T)‖ | T |+| T^* |‖
amp;≤(1)/(6) ‖ | T |²+ | T^* |² ‖ + (1)/(3) ω(T)‖ | T |+| T^* |‖, which refines the recent inequality obtained by Kittaneh and Moradi in \citeKM.

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