Cauchy-Bunyakovskii inequality

Lemma 2 For any positive self-adjoint operator A in a real Hilbert space the generalized Cauchy-Bunyakovskii inequality holds ... 

The Cauchy-Bunyakovskii inequality and the e-inequality. In the sequel we shall need the well-known Cauchy-Bunyakovskii inequality... 

Let us estimate the sums on the right-hand side of the preceding relation with the aid of the Cauchy-Bunyakovskii inequality ... 

To majorize the right-hand side, we make use of the Cauchy-Bunyakovskii inequality and the e-inequality a6 < a + i with e = permitting... 

By applying successively the Cauchy-Bunyakovskii inequality and the -inequality we arrive at the chain of the relations... 

Proof The energy identity (13) is involved at the first stage. Estimation of it.s right-hand side 2r(9j, y ) is stipulated by successive use of the generalized Cauchy-Bunyakovskii inequality and the e-inequality... 

The generalized Cauchy-Bunyakovskii inequality and the gr-inequality together yield... 

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