Norm inequalities for hyperaccretive quasinormal operators, with extensions of the arithmetic-geometric means inequality

Abstract

Let (Formula presented.) be symmetrically norming (s.n.) functions, let (Formula presented.) be the ideal of compact Hilbert space operators, associated with the s.n. function Ψ, (Formula presented.) and let (Formula presented.) be such that A, B are accretive and (Formula presented.) Then (Formula presented.) as well, and (Formula presented.) under any of the following conditions: (Formula presented.) and A (resp. (Formula presented.)) is quasinormal operator with its adjoint operator being 2-hyperaccretive and having the injective real part; if both A and (Formula presented.) are quasinormal operators with its adjoint operators being 2-hyperaccretive operators and having injective real parts. Also, for (Formula presented.) which are such that (Formula presented.) for (Formula presented.) for s.n. functions (Formula presented.) for bounded Hilbert space operators (Formula presented.) such that A is (Formula presented.) -hyperaccretive and (Formula presented.) is (Formula presented.) -hyperaccretive, satisfying (Formula presented.) then there exists (Formula presented.) (Formula presented.) and (Formula presented.) (Formula presented.) hold under any of the following conditions: if (Formula presented.) and A or (Formula presented.) is normal (in which case (Formula presented.)), if both A and (Formula presented.) are normal (in which case (Formula presented.)), if (Formula presented.) and (Formula presented.).