【摘 要】
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We present upper bounds of eigenvalues for finite and infinite dimensional Cauchy-Hankel tensors.It is proved that an m-order infinite dimensional Canchy-Hankel tensor defines a bounded and positively (m-1)-homogeneous operator from l1 into lp (1 ＜ p ＜ ∞)
【机 构】
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School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,China;School of Mathematic
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We present upper bounds of eigenvalues for finite and infinite dimensional Cauchy-Hankel tensors.It is proved that an m-order infinite dimensional Canchy-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.
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