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The applications of Cauchy-Schwartz inequality for Hilbert modules to elementary operators and I.P.T.I. transformers

Kečkić Dragoljub J. (University of Belgrade, Faculty of Mathematics, Beograd, Serbia), keckic@matf.bg.ac.rs

We apply the inequality |‹x,y›| ≤ ||x|| ‹y,y›1/2 to give an easy and elementary proof of many operator inequalities for elementary operators and inner type product integral transformers obtained during last two decades, which also generalizes many of them.

Keywords: Cauchy Schwartz inequality, unitarily invariant norm, elementary operator, inner product type transformers.

Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174034