An Operator Extension of Čebyšev Inequality

Some operator inequalities for synchronous functions that are related to the čebyšev inequality are given. Among other inequalities for synchronous functions it is shown that ∥ø(f(A)g(A)) - ø(f(A))ø(g(A))∥ ≤ max{║ø(f2(A)) - ø2(f(A))║, ║ø)G2(A)) - ø2(g(A))║} where A is a self-adjoint and compact operator on B(ℋ ), f, g ∈ C (sp (A)) continuous and non-negative functions and ø: B(ℋ ) → B(ℋ ) be a n-normalized bounded positive linear map. In addition, by using the concept of quadruple D-synchronous functions which is generalizes the concept of a pair of synchronous functions, we establish an inequality similar to čebyšev inequality.

On an Extension Problem for Contractive Block Hankel Operator Matrices

The paper deals with an operator extension problem for contractive block Hankel operators which arose in the context of the operator version of the classical Nehari interpolation problem. V.M. Adamjan, D.Z. Arov, and M.G. Krein [5] obtained that the solution set of this operator extension problem is an operator ball. Hereby, they constructed the parameters of this operator ball via a regularization procedure using the corresponding expressions of the first studied nondegenerate case. The main aim of this paper is to derive more explicit formulas for the parameters of this operator ball. Hereby we use Moore-Penrose inverses of bounded linear operators in Hilbert space.

VERTEX OPERATOR EXTENSION OF CASIMIR WAN ALGEBRAS

We give an extension of Casimir WAN algebras including a vertex operator which depends on non-simple roots of AN-1.