Decomposable bilinear numerical radii

AbstractLet A be an n-square normal matrix over C, and Qm, n be the set of strictly increasing integer sequences of length m chosen from 1,…, n. For α,β∈Qm, n denote by A[α|β] the submatrix obtained from A by using rows numbered α and columns numbered β. For k∈{0,1,…,m} write z.sfnc;α∩β|=k if there exists a rearrangement of 1,…,m, say i1,…,ik, ik+1,…,im, such that α(ij)=β(ij), j=1,…,k, and {α(ik+1),…,α(im)};∩{β(ik+1),…,β(im)}=ø. Let be the group of n-square unitary matrices. Define the nonnegative number ϱk(A)= maxU∈|det(U∗AU) [α|β]|, where |α∩β|=k. Theorem 1 establishes a bound for ϱk(A), 0⩽k