## 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

### Keywords:

inner product spaces; Schwarz’s inequality
Full Text:

### References:

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