Upper bounds for eigenvalues of Cauchy-Hankel tensors

We present upper bounds of eigenvalues for finite and infinite dimensional Cauchy-Hankel tensors. It is proved that an m-order infinite dimensional Cauchy-Hankel tensor defines a bounded and positively (m − 1)-homogeneous operator from l1 into lp (1 < p < ∞), and two upper bounds of corresponding positively homogeneous operator norms are given. Moreover, for a fourth-order real partially symmetric Cauchy-Hankel tensor, sufficient and necessary conditions of M-positive definiteness are obtained, and an upper bound of M-eigenvalue is also shown.