Unitarily invariant norm inequalities involving G₁ operators

الأصل · EN

In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove align* f(A)Xg(B)± g(B)Xf(A)₂≤ (I+|A|)X(I+|B|)+(I+|B|)X(I+|A|)/dₐdB₂, align* where A, B, Xₙ such that A, B are Hermitian with σ(A)∪σ(B) and f, g are analytic on the complex unit disk D, g(0)=f(0)=1, Re(f)>0 and Re(g)>0.