A new proof of an inequality of Bohr for Hilbert space operators
The authors give a simple proof of Bohr's inequality for Hilbert space operators, i.e., \[ |A-B|^{2}+|(1-p)A-B|^{2}\leq p|A|^{2}+q|B|^{2} \] for \(\frac{1}{p}+\frac{1}{q}=1\) and \(A,B\in B(H)\). In the proof, which simplifies the one in [\textit{W.--S.\thinspace Cheung} and \textit{J.\,Pečarić}, J.~Math.\ Anal.\ Appl.\ 323, 403--412 (2006; Zbl 1108.26018)], the authors point out that the equality \[ p|A|^{2}+q|B|^{2}=|A-B|^{2}+\frac{1}{p-1}|(p-1)A+B|^{2} \] is important.
scientific article; zbMATH DE number 5505639