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1
Content available remote Some properties of the spectral radius of a set of matrices
100%
Czornik A. , Jurgas P.
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nr 2
183-188
EN
In this paper we show new formulas for the spectral radius and the spectral subradius of a set of matrices. The advantage of our results is that we express the spectral radius of any set of matrices by the spectral radius of a set of symmetric positive definite matrices. In particular, in one of our formulas the spectral radius is expressed by singular eigenvalues of matrices, whereas in the existing results it is expressed by eigenvalues.
2
Content available remote Minimal incomplete norms on Banach algebras
100%
Meyer M. J.
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nr 1
77-85
EN
We study the family of all not necessarily complete algebra norms on a semisimple Banach algebra as a partially ordered set and investigate the existence and properties of minimal elements.
3
Content available remote Regularity of the multidimensional scaling functions: estimation of the $L^{p}$-Sobolev exponent
88%
Kotowicz J.
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nr 4
431-447
EN
The relationship between the spectral properties of the transfer operator corresponding to a wavelet refinement equation and the $L^p$-Sobolev regularity of solution for the equation is established.
4
Content available remote Asymptotic stability in the Schauder fixed point theorem
75%
Shih M.-H. , Wu J.-W.
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nr 2
143-148
EN
This note presents a theorem which gives an answer to a conjecture which appears in the book Matrix Norms and Their Applications by Belitskiĭ and Lyubich and concerns the global asymptotic stability in the Schauder fixed point theorem. This is followed by a theorem which states a necessary and sufficient condition for the iterates of a holomorphic function with a fixed point to converge pointwise to this point.
5
Content available remote Some properties of the spectral radius of a set of matrices
75%
Czornik A. , Jurgaś P.
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tom Vol. 16, no 2
183-188
EN
In this paper we show new formulas for the spectral radius and the spectral subradius of a set of matrices. The advantage of our results is that we express the spectral radius of any set of matrices by the spectral radius of a set of symmetric positive definite matrices. In particular, in one of our formulas the spectral radius is expressed by singular eigenvalues of matrices, whereas in the existing results it is expressed by eigenvalues.
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