The order bounded Stevi-Sharma operators between weighted Dirichlet spaces are characterized, which generalizes the previous result obtained by Lin and his colleagues.

Let (X) denote the -operator radius of a bounded linear operator X on a finite dimensional Hilbert space H , where 0 < 2 .In this article, we present -operator radii generalizations of various numerical radius commutator inequalities, includingand the arithmetic-geometric mean inequality:under various conditions on X and Y .

This paper focuses on establishing new upper bounds for the numerical radius of operators on Hilbert spaces by utilizing the Moore-Penrose inverse and the generalized Cartesian decomposition.The obtained estimates enhance the existing body of knowledge and are systematically compared with results from the current literature.Our findings not only extend but also unify several recent contributions, offering a broader and more cohesive framework for understanding numerical radius inequalities.Through the application of the generalized Cartesian decomposition, we provide deeper insights into the behavior of numerical radii, building upon previous research and opening new directions for further investigation in this field.

Let X and Y be two infinite dimensional Banach spaces and B(X ) (resp.B(Y ) ) be the algebra of bounded linear operators on X (resp.Y ).For T B(X ) and x X , T (x) denotes the local spectrum of T at x .Fix an integer k 2 , and let A 1 * A 2 * ... * A k stand for a generalized product of any k operators A 1 , A 2 , ... , A k B(X ) .Given two nonzero vectors x 0 X and y 0 Y , in this paper, we characterize all surjective maps : B(X ) B(Y ) which satisfy A 1 * A 2 * ... * A k (x 0 ) = (A 1 )