Some Versions of Anderson’s and Maher’s Inequalities Ii
نویسنده
چکیده
We are interested in the investigation of the orthogonality (in the sense of Birkhoff) of the range of an elementary operator and its kernel. 1. Introduction. Let H be a separable infinite-dimensional complex Hilbert space and let B(H) denote the algebra of all bounded operators on H into itself. Given A, B ∈ B(H), we define the generalized derivation δ A,B : B(H) B(H) by δ A,B (X) = AX −XB and the elementary operator derivation ∆ A,B : B(H) B(H)
منابع مشابه
Some Versions of Anderson’s and Maher’s Inequalities I
We prove the orthogonality (in the sense of Birkhoff) of the range and the kernel of an important class of elementary operators with respect to the Schatten p-class. 1. Introduction. Let H be a separable infinite-dimensional complex Hilbert space and let B(H) denote the algebra of all bounded operators on H into itself. Given A, B ∈ B(H), we define the generalized derivation δ A,B : B(H) B(H) b...
متن کاملSome Weighted Integral Inequalities for Generalized Conformable Fractional Calculus
In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss type inequalities for conformable fractional integrals which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions.
متن کاملImprovements of Young inequality using the Kantorovich constant
Some improvements of Young inequality and its reverse for positive numbers with Kantorovich constant $K(t, 2)=frac{(1+t)^2}{4t}$ are given. Using these inequalities some operator inequalities and Hilbert-Schmidt norm versions for matrices are proved. In particular, it is shown that if $a, b$ are positive numbers and $0 leqslant nu leqslant 1,$ then for all integers $ kgeqsl...
متن کاملOn the $s^{th}$ Derivative of a Polynomial-II
The paper presents an $L^{r}-$ analogue of an inequality regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle of arbitrary radius but greater or equal to one. Our result provides improvements and generalizations of some well-known polynomial inequalities.
متن کاملStability results for some geometric inequalities and their functional versions ∗
The Blaschke Santaló inequality and the Lp affine isoperimetric inequalities are major inequalities in convex geometry and they have a wide range of applications. Functional versions of the Blaschke Santaló inequality have been established over the years through many contributions. More recently and ongoing, such functional versions have been established for the Lp affine isoperimetric inequali...
متن کامل