Extension of Euclidean operator radius inequalities

Original · EN

To extend the Euclidean operator radius, we define wₚ for an n-tuples of operators (T₁,, Tₙ) in B(H) by wₚ(T₁,,Tₙ):= ₓ ₌₁ (∑ᵢ₌₁ⁿ| Tᵢ x, x |ᵖ)1p for p≥1. We generalize some inequalities including 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 nonnegative continuous functions on [0,∞) satisfying f(t) g(t) =t for all t∈ [0,∞), then equation* wₚrp(A₁₁B₁,,AₙₙBₙ) ≤ 1/2 i=1n∑ ([Bᵢ²(Tᵢ) Bᵢ] rp+[Aᵢ²(Tᵢ) Aᵢ] rp) equation* for all p≥ 1, r≥ 1 and operators in B(H).