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Operator refinements of Schwarz inequality in inner product spaces. (English) Zbl 1430.46018

Summary: Some improvements of the celebrated Schwarz inequality in complex inner product spaces in terms of selfadjoint operators \(0\leq A\leq 1_H\) are given. Applications for orthonormal families of vectors are also provided.

MSC:

46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
26D15 Inequalities for sums, series and integrals
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