AN OPERATOR EXTENSION OF CEBYSEV INEQUALITY

作者：Moradi Hamid Reza^*; Omidvar Mohsen Erfanian; Dragomir Silvestru Sever

来源：Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, 2017, 25(2): 135-147.

DOI：10.1515/auom-2017-0025

• Cebysev inequality
• self-adjoint operators
• synchronous (asynchronous) functions
• functions of self-adjoint operators
• positive linear map

Some operator inequalities for synchronous functions that are related to the Cebysev inequality are given. Among other inequalities for synchronous functions it is shown that
parallel to phi(f (A)g(A))-phi(f (A))phi(g(A))parallel to <= max {parallel to phi(f(2)(A))-phi(2) (f (A))parallel to, parallel to phi(g(2)(A))-phi(2)(g (A))parallel to}
where A is a self-adjoint and compact operator on B (H), f, g is an element of C (sp (A)) continuous and non -negative functions and phi : 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 Cebysev inequality.

• 出版日期2017