Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/32933
Title: Infinite and finite dimensional Hilbert tensors
Authors: Song, Y
Qi, L 
Keywords: Eigenvalue
Hilbert tensor
Positively homogeneous
Spectral radius
Issue Date: 2014
Publisher: North-Holland
Source: Linear algebra and its applications, 2014, v. 451, p. 1-14 How to cite?
Journal: Linear algebra and its applications 
Abstract: For an m-order n-dimensional Hilbert tensor (hypermatrix) H n=(Hi1i2⋯im), Hn=(H i1i2⋯im=1i1+i2+⋯+ im-m+1,i1,⋯,im=1,2,⋯,n its spectral radius is not larger than nm-1sinπn, and an upper bound of its E-spectral radius is nm2sinπn. Moreover, its spectral radius is strictly increasing and its E-spectral radius is nondecreasing with respect to the dimension n. When the order is even, both infinite and finite dimensional Hilbert tensors are positive definite. We also show that the m-order infinite dimensional Hilbert tensor (hypermatrix) H∞=( H n=(Hi1i2⋯im) defines a bounded and positively (m-1)-homogeneous operator from l1 into lp (1<p<∞), and the norm of corresponding positively homogeneous operator is smaller than or equal to π√6.
URI: http://hdl.handle.net/10397/32933
ISSN: 0024-3795
EISSN: 1873-1856
DOI: 10.1016/j.laa.2014.03.023
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