Extensions of Euclidean operator radius inequalities - Moslehian, Mohammad Sal; Sattari, Mostafa; Shebrawi, Khalid (MATHEMATICA SCANDINAVICA, 2017)
To extend the Euclidean operator radius, we define w_p for an n-tuple of operators (T_1,…,T_n) in B(H) by w_p(T_1,…,T_n):= _x Vert =1 (_i=1^nT_i x, x vert^p)^1/p for p≥1. We generalize some inequalities including the Euclidean operator radius of two operators to those involving w_p. Further we obtain some lower and upper bounds for w_p. 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 equation* w_p^rp( A_1^*T_1B_1, … ,A_n^*T_nB_n) ≤ n^r-1 2 _i=1^n [ B_i^*f^2( T_i vert ) B_i] ^rp + [ A_i^*g^2( T_i^* vert ) A_i]^rp Vert, equation* for all p≥ 1, r≥ 1 and operators in B(H).