Čebyšev's type inequalities for functions of selfadjoint operators in Hilbert spaces

Abstract

Abstract. Some inequalities for continuous synchronous (asynchronous) functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved operators, are given.

A survey of Jensen type inequalities for functions of selfadjoint operators in Hilbert spaces

“…We use the following Čebyšev type inequality for functions of operators established by the author in [16]: …”

Cebysev’s type inequalities for positive linear maps of selfadjoint operators in Hilbert spaces

“…The following result that is related to the Čebyšev inequality also holds [14] (see also [13, p. 73] …”

“…The following result provides an inequality of Čebyšev type for functions of selfadjoint operators [14] (see also [13, p. 73] or [15, p. 73 …”

New bounds for the Cebysev functional of two functions of selfadjoint operators in Hilbert spaces

“…The following result provides an inequality ofČebyšev type for functions of selfadjoint operators, see [2]: for any x ∈ H with x = 1.…”