Extensions of Euclidean operator radius inequalities

To extend the Euclidean operator radius, we define wₚ for an n-tuple of operators (T₁, , Tₙ) in B (H) by wₚ (T₁, , Tₙ): = ₗ =₁ (₈=₁^n Tᵢ x, x ᵖ) ^1/p for p1. 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 equation* w₏^rp (A₁^*T₁B₁, , A₍^*T₍B₍) n^r-12 ₈=₁ⁿ [ B₈^*f^2 (T₈) B₈ ^rp + A₈^*g^2 (T₈^*) A₈^rp, equation* for all p 1, r 1 and operators in B (H).