An Operator Karamata Inequality

作者：Moslehian Mohammad Sal^*; Niezgoda Marek; Rajic Rajna

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2014, 37(4): 949-954.

• Karamata inequality
• operator inequality
• positive operator
• unital C*-algebra
• state

We present an operator version of the Karamata inequality. More precisely, we prove that if A is a selfadjoint element of a unital C*-algebra A, rho is a state on A, the functions f,g are continuous on the spectrum sigma(A) of A such that 0 %26lt; m(1) %26lt;= f(s) %26lt;= M-1, 0 %26lt; m(2) %26lt;= g(s) %26lt;= M-2 for all s is an element of sigma(A) and K = (root m(1)m(2) +root M1M2)/(root m(1)M(2)) + root M(1)m(2), then %26lt;br%26gt;K-2 %26lt;= rho(f(A)g(A))/rho(f(A)rho(g(A)) %26lt;= K-2. %26lt;br%26gt;We also give some applications.

• 出版日期2014