Norm Inequalities for Self-Adjoint Derivations

Cauchy–Schwarz norm inequalities for weak∗-integrals of operator valued functions

“…AX * B d * m as n-N: According to(17) an appeal to the lower semi-continuity of jj Á jj p proves Theorem 3.3 with * A; * B instead of A; B: In other words, we now have…”

“…It is the arithmetic-geometric-logarithmic (56),(74) and Young (66) inequalities that have been under especially intensive investigation and a very good account can be found in [2,6,16]. Power and other various natural mean operator inequalities are investigated in [18,20,21,16], perturbation and generalized derivations norm inequalities in [1,11,17], and different Cauchy-Schwarz inequalities in [9,18,19], with the numerous references therein.…”

“…The arithmetic-geometric mean inequality for operators (see [8]) has had considerable applications in Operator Theory (see [9,17]) and different proofs are known. Here, we present one via operator integrals.…”

Unitarily invariant norm inequalities for elementary operators involving G1 operators

“…[4,13]. For some other perturbation results the reader is referred to [10,12]. In this paper, we present some upper bounds for |||f (A)Xg(B) ± X|||, where A, B are G 1 operators, ||| · ||| is a unitarily invariant norm and f, g ∈ H. Further, we find some new upper bounds for the the Schatten 2-norm of f (A)X ± Xg(B).…”

On Norm Estimates for Derivations in Norm-Attainable Classes

“…D and D s were investigated and approximated finite-dimension (AF )C * -algebra in that context and an example was given to show certain estimates. The results of [44] showed that for a certain Von Neumann algebra U, In [14] the researcher considered λ(M) defined as the smallest number Z 2 of Z that satisfy [Z * , Z] = M and showed that 1 ≤ λ(M) ≤ 2. Matej [28] estimated the distance of d 1 and d 2 to the generalized derivations and the normed algebra of P and considered the cases when P is an ultraprime, when d 1 = d 2 and P are ultrasemiprime and when P is a Von Neumann algebra we have the equation…”