Resumen de Extensions of Euclidean operator radius inequalities

Mohammad Sal Moslehian, Mostafa Sattari, Khalid Shebrawi

• To extend the Euclidean operator radius, we define wp for an n-tuple of operators (T1,…,Tn) in B(H) by wp(T1,…,Tn):=sup∥x∥=1(∑ni=1|⟨Tix,x⟩|p)1/p for p≥1. We generalize some inequalities including the Euclidean operator radius of two operators to those involving wp. Further we obtain some lower and upper bounds for wp. Our main result states that if f and g are non-negative continuous functions on [0,∞) satisfying f(t)g(t)=t for all t∈[0,∞), then wrpp(A∗1T1B1,…,A∗nTnBn)≤nr−12∥∥∑i=1n[B∗if2(|Ti|)Bi]rp+[A∗ig2(|T∗i|)Ai]rp∥∥, for all p≥1, r≥1 and operators in B(H).