On the local spectral radius in partially ordered Banach spaces
Mirosława Zima (1999)
Czechoslovak Mathematical Journal
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Mirosława Zima (1999)
Czechoslovak Mathematical Journal
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Jan Ligęza (2005)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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We study the existence of positive solutions of the integral equation in both and spaces, where and . Throughout this paper is nonnegative but the nonlinearity may take negative values. The Krasnosielski fixed point theorem on cone is used.
Vladimír Müller (1997)
Annales Polonici Mathematici
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We prove the -spectral radius formula for n-tuples of commuting Banach algebra elements
Mirosława Zima (2014)
Czechoslovak Mathematical Journal
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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,...
Trung Dinh Tran (2002)
Applications of Mathematics
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The paper defines and studies the Drazin inverse for a closed linear operator in a Banach space in the case that belongs to a spectral set of the spectrum of . Results are applied to extend a result of Krein on a nonhomogeneous second order differential equation in a Banach space.
M. T. Karaev (2006)
Colloquium Mathematicae
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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 and a suitable bounded linear operator A on a Banach space X.
Nikolai Nikolov, Pascal J. Thomas (2008)
Annales Polonici Mathematici
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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 to the isospectral variety at A. In the case of Ω₃, the zero set of the Kobayashi-Royden pseudometric is completely described.
Victor S. Shulman, Yuriĭ V. Turovskii (2002)
Studia Mathematica
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The formula 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), is the Hausdorff spectral radius (connected with the Hausdorff measure of noncompactness) and r(M) is the Berger-Wang radius.