Publications de l'Institut Mathématique (Beograd)
Vol. 73(87), pp. 149-154 (2003)
ON GENERALIZED INEQUALITIES OF HEINZ, HALMOS AND BERNSTEIN
C.-S. LinDepartment of Mathematics, Bishop's University, Lennoxville, Quebec, J1M 1Z7 Canada
Abstract: We present generalized inequalities of Heinz, Halmos and Bernstein. It is proved that they are all equivalent to one another. In fact they are are all equivalent to the Cauchy--Schwarz inequality. Equality condition and the bound of inequality are established.
Classification (MSC2000): 47A63; 47A30
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