Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614907 | Journal of Mathematical Analysis and Applications | 2016 | 13 Pages |
Abstract
We prove singular value inequalities for convex functions of products and sums of operators that generalize the arithmetic–geometric mean inequality for operators. Among other results, we prove that if AiAi, BiBi, XiXi, YiYi, i=1,…,ni=1,…,n are operators on a complex separable Hilbert space such that |Xi|2+|Yi|22n≤I, i=1,…,ni=1,…,n and if f is a nonnegative increasing convex function on [0,∞)[0,∞) satisfying f(0)=0f(0)=0, thensj(f(|∑i=1nAiXiYi⁎Bi⁎|))≤12sj(⨁k=1n(Xk⁎(∑i=1nf(|Ai⁎Ak|))Xk+Yk⁎(∑i=1nf(|Bi⁎Bk|))Yk)) for j=1,2,…j=1,2,… .
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Omar Hirzallah,