Extension of Euclidean operator radius inequalities

2015/01/31 by Moslehian, M. S., Sattari, M., Shebrawi, K. · 1 citation
#47A12 #47A30 #47A63 #47B15 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1502.00083

Abstract

To extend the Euclidean operator radius, we define w_p for an n-tuples of operators (T₁,…, T_n) in \mathbbB(\mathscrH) by w_p(T₁,…,T_n):= sup_{‖ x ‖ =1} (∑_i=1ⁿ| ⟨ T_i x, x ⟩ |^p )^\frac1p for p≥1. We generalize some inequalities including 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 nonnegative continuous functions on [ 0,∞ ) satisfying f( t) g(t) =t for all t∈ [ 0,∞ ) , then w_p^rp( A₁^∗ T₁B₁,… ,A_n^∗ T_nB_n) ≤ (1)/(2)\Vert \underseti=1\oversetn∑ ( [ B_i^∗ f²( \vert T_i\vert ) B_i] ^rp+[ A_i^∗ g²( \vert T_i^∗ \vert ) A_i] ^rp)\Vert for all p≥ 1, r≥ 1 and operators in \mathbbB(\mathscrH).

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