Buse, ConstantinDragomir, Sever S.2020-02-202020-02-202001-11-23Buse, C., & Dragomir, S. S. (2001). A theorem of Rolewicz's type for measurable evolution families in Banach spaces. <i>Electronic Journal of Differential Equations, 2001</i>(70), pp. 1-5.1072-6691https://hdl.handle.net/10877/9318Let φ be a positive and non-decreasing function defined on the real half-line and U be a strongly measurable, exponentially bounded evolution family of bounded linear operators acting on a Banach space and satisfing a certain measurability condition as in Theorem 1 below. We prove that if φ and U satisfy a certain integral condition (see the relation 1 from Theorem 1 below) then U is uniformly exponentially stable. For φ continuous and U strongly continuous and exponentially bounded, this result is due to Rolewicz. The proofs uses the relatively recent techniques involving evolution semigroup theory.Text6 pages1 file (.pdf)enAttribution 4.0 InternationalEvolution family of bounded linear operatorsEvolution operator semigroupRolewicz's theoremExponential stabilityArticle