Generalized Euclidean operator radius inequalities of a pair of bounded linear operators

Let B (H) represent the C^*-algebra, which consists of all bounded linear operators on H, and let N (. ) be a norm on B (H). We define a norm w (₍, ₄) (. ,. ) on B² (H) by w (₍, ₄) (B, C) =|₁|²+₂|²1 R N ( (e^i (₁B+₂C) ) ), for every B, C (H) and ₁, ₂. We investigate basic properties of this norm and prove some bounds involving it. In particular, when N (. ) is the Hilbert-Schmidt norm, we prove some Hilbert-Schmidt Euclidean operator radius inequalities for a pair of bounded linear operators.