[PDF] Top 20 Vector Inequalities for Powers of Some Operators in Hilbert Spaces

... Vector inequalities for powers of some operators in Hilbert spaces with applications for operator norm, numerical radius, commutators and self- commutators are given1. The numerical rang[r] ... See full document

... the Hilbert space H and A is a self-adjoint operator with SpA ⊆ m, M, and provide different bounds for some classes of continuous functions f : m, M → ...for some particular cases including the power ... See full document

... paper some vector in- equalities for two operators A, B for which the operator Re (B ∗ A) is nonnega- tive in the operator order that are related to the inequality ...radius inequalities are ... See full document

... Some norm inequalities for sequences of linear operators defined on Hilbert spaces that are related to the classical Schwarz inequality are given.. Applications for vector inequalities a[r] ... See full document

... the Hilbert space (H; h :; : i ) with the spectrum Sp (U ) included in the interval [m; M] for some real numbers m < M and let f E g 2R be its spectral ... See full document

... complex Hilbert space (H; h :; : i ) : The Gelfand map establishes a -isometrically isomorphism between the set C (Sp (A)) of all continuous functions de…ned on the spectrum of A; denoted Sp (A) ; an the C ... See full document

... Furuta inequalities for power series of bounded linear operators in Hilbert spaces are ...normal operators and some functions of interest such as the exponential, hyperbolic and ... See full document

... Let B (H ) denote the C ∗ −algebra of all bounded linear operators on a complex Hilbert space H with inner product h·, ·i. For A ∈ B (H ) , let w (A) and kAk denote the numerical radius and the usual ... See full document

... Remark 2.1. The inequality (2.3) is obviously not as good as the first part of (1.12). However it is the natural alternative of Jensen’s inequality for trace and provides simple and nice examples for various convex ... See full document

... Let (H, h·, ·i) be a Hilbert space over the real or complex number field K ( K = R , C ) . Let B (H) denote the C ∗ −algebra of all bounded linear operators on a complex Hilbert space H. For A ∈ B (H ... See full document

... the interval [0, R) and since the function ψ(t) := ∥ (1 − t)T + tV ∥ is convex on [0, 1] we have that f a ′ ◦ ψ is also convex on [0, 1]. Utilising the Hermite- Hadamard inequality for convex functions (see for instance ... See full document

... paper some inequalities for the nu- merical radius of functions of operators defined by power series, which incorporate many fundamental functions of interest such as the exponential function, ... See full document

... new inequalities for the operator norm and numerical radius of sums of bounded linear operators in Hilbert ...linear operators and their applications for the Cartesian decomposition of an ... See full document

... Dragomir, Some inequalities of the Gr¨ uss type for the numerical radius of bounded linear operators in Hilbert spaces, Preprint, RGMIA Res.. Gustafson and D.K.M.[r] ... See full document

... Let A be a selfadjoint linear operator on a complex Hilbert space (H; h., .i) . The Gelfand map establishes a ∗-isometrically isomorphism Φ between the set C (Sp (A)) of all continuous functions defined on the ... See full document

... establish some connections that exist between the numerical radius w (A) , operator norm kAk and the semi- inner products hA, Ii p,n and hA, Ii p,w with p ∈ {i, s} that can be naturally defined on the Banach ... See full document

... involved operators A and B (or certain expressions constructed with these operators), we establish in this paper some natural inequalities of the ... See full document

... Theorem 6. Let I be an interval and f : I → R be a convex and differentiable function on ˚ I (the interior of I) whose derivative f 0 is continuous on ˚ I. If A is a selfadjoint operator on the Hilbert space H ... See full document

... Let A be a selfadjoint linear operator on a complex Hilbert space (H; h., .i) . The Gelfand map establishes a ∗-isometrically isomorphism Φ between the set C (Sp (A)) of all continuous functions defined on the ... See full document

... related inequalities in inner product spaces (II), ...Dragomir, Inequalities for the norm and the numerical radius of linear operators in Hilbert spaces, Demonstratio Mathematica ... See full document