A Gruss inequality for n-positive linear maps

作者：Moslehian Mohammad Sal; Rajic Rajna^*

来源：Linear Algebra and Its Applications, 2010, 433(8-10): 1555-1560.

DOI：10.1016/j.laa.2010.06.006

• Gruss inequality
• Operator inequality
• Positive operator
• C*-algebra
• Completely positive map
• n-positive map

Let A be a unital C*-algebra and let phi : A -> B(H) be a unital n-positive linear map between C*-algebras for some n >= 3. We show that
parallel to phi(AB) - phi(A)phi(B)parallel to <= Delta(A, parallel to center dot parallel to) Delta(B, parallel to center dot parallel to)
for all operators A, B is an element of A, where Delta(C, parallel to center dot parallel to) denotes the operator norm distance of C from the scalar operators.

• 出版日期2010-12-15