DOIAbstract
AbstractLet Cn be the linear space of complex column vectors with n coordinates associated with the usual inner product. Denote by Λk the set of all k-tuples of orthonormal vectors in Cn. Given a real number p⩾ 1and an n × n complex matrix A with eigenvalues λ1,…,λn, we define ρp − k = max∑j = 1k∣λij ∣p1p :1⩽i1<·<ik⩽nrp − k = max∑i = 1k∣xi∗Axi∣p1p :{x1,…,xk}∈Λk and ‖A‖p−k = max∑i = 1k∣xi∗Ayi∣p1p :{x1,…,xk},{y1,…,yk}∈Λk as the (p-k)-spectral radius, (p-k)-numerical radius, and (p-k)-spectral norm of A, respectively. For k = 1 they are the classical spectral radius, numerical radius, and spectral norm of A. In this note we study the matrices for which ρp-k(A) = rp-k(A), ρp-k(A)=‖A‖p-k, or rp-k(A) = ‖A‖p-k. Moreover, the norm properties of rp-...
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