Displaying similar documents to “Applications of the spectral radius to some integral equations”

Remarks on existence of positive solutions of some integral equations

Jan Ligęza (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica


We study the existence of positive solutions of the integral equation x ( t ) = μ 0 1 k ( t , s ) f ( s , x ( s ) , x ' ( s ) , ... , x ( n - 1 ) ( s ) ) d s , n 2 in both C n - 1 [ 0 , 1 ] and W n - 1 , p [ 0 , 1 ] spaces, where p 1 and μ > 0 . Throughout this paper k is nonnegative but the nonlinearity f may take negative values. The Krasnosielski fixed point theorem on cone is used.

On the joint spectral radius

Vladimír Müller (1997)

Annales Polonici Mathematici


We prove the p -spectral radius formula for n-tuples of commuting Banach algebra elements

Spectral radius inequalities for positive commutators

Mirosława Zima (2014)

Czechoslovak Mathematical Journal


We establish several inequalities for the spectral radius of a positive commutator of positive operators in a Banach space ordered by a normal and generating cone. The main purpose of this paper is to show that in order to prove the quasi-nilpotency of the commutator we do not have to impose any compactness condition on the operators under consideration. In this way we give a partial answer to the open problem posed in the paper by J. Bračič, R. Drnovšek, Y. B. Farforovskaya, E. L. Rabkin,...

On the spectral multiplicity of a direct sum of operators

M. T. Karaev (2006)

Colloquium Mathematicae


We calculate the spectral multiplicity of the direct sum T⊕ A of a weighted shift operator T on a Banach space Y which is continuously embedded in l p and a suitable bounded linear operator A on a Banach space X.

On the zero set of the Kobayashi-Royden pseudometric of the spectral unit ball

Nikolai Nikolov, Pascal J. Thomas (2008)

Annales Polonici Mathematici


Given A∈ Ωₙ, the n²-dimensional spectral unit ball, we show that if B is an n×n complex matrix, then B is a “generalized” tangent vector at A to an entire curve in Ωₙ if and only if B is in the tangent cone C A to the isospectral variety at A. In the case of Ω₃, the zero set of the Kobayashi-Royden pseudometric is completely described.

Formulae for joint spectral radii of sets of operators

Victor S. Shulman, Yuriĭ V. Turovskii (2002)

Studia Mathematica


The formula ϱ ( M ) = m a x ϱ χ ( M ) , r ( M ) is proved for precompact sets M of weakly compact operators on a Banach space. Here ϱ(M) is the joint spectral radius (the Rota-Strang radius), ϱ χ ( M ) is the Hausdorff spectral radius (connected with the Hausdorff measure of noncompactness) and r(M) is the Berger-Wang radius.