operator extension
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2017 ◽  
Vol 25 (2) ◽  
pp. 135-147
Author(s):  
Hamid Reza Moradi ◽  
Mohsen Erfanian Omidvar ◽  
Silvestru Sever Dragomir

Abstract 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.


2010 ◽  
Vol 46 (12) ◽  
pp. 3990-4000 ◽  
Author(s):  
Ermanno Cardelli ◽  
Edward Della Torre ◽  
Antonio Faba

Analysis ◽  
2005 ◽  
Vol 25 (1) ◽  
Author(s):  
Bernd Fritzsche ◽  
Bernd Hirstein ◽  
Jürgen Lorenz

AbstractThe 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.


1998 ◽  
Vol 13 (33) ◽  
pp. 2645-2652
Author(s):  
H. T. ÖZER

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


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