Some generalizations of numerical radius on off-diagonal part of 2× 2 operator matrices

Original · EN

We generalize several inequalities involving powers of the numerical radius for off-diagonal part of 2×2 operator matrices of the form T=[arraycc 0&B, C&0 array], where B, C are two operators. In particular, if T=[arraycc 0&B, C&0 array], then we get align* 1 232(r-1){ μ, η } ≤ wʳ(T)≤ 12ʳ⁺¹ { μ, η }, align* where r≥ 2 and μ=|(C-B*)+i(C+B*)|ʳ+|(B*-C)+i(C+B*)|ʳ, η=|(B-C*)+i(B+C*)|ʳ+|(C*-B)+i(B+C*)|ʳ.