On Bergstrom inequality for commuting gramian normal operators

Abstract

Abstract. We hereby present a variant of Bergstrom inequality for gramian normal operators on Loynes spaces and Hilbert spaces, as well as several consequences.Mathematics subject classification (2010): Primary 47A45; Secondary 42B10.

Several inequalities for norm

“…Proof. Starting with the inequality (6) from Theorem 6, see [4], by similary calculus we obtain the desired inequality.…”

“…In the first part of this section we reformulate inequalities from [4] in the case of the classical norm given by the scalar product in Hilbert spaces and then we extend some inequalities given in [13] for positive invertible operators on H.…”

“…Proof. We take into account the inequality (1) from [4] and then for every x ∈ H, considering the inner product, we have:…”

“…Proof. We use the same method as in Theorem 1 and take into account the inequality from Proposition 2, see [4].…”

Several refinements and counterparts of Radon's inequality

“…Refinements of Bergström's inequality were established by many authors, in particular, by Mȃrghidanu-Barrero-Rȃdulescu (see [11]) and Pop (see [16]). In [4] we can find interesting applications of these inequalities developed by Ciurdariu. In [12],…”