Bounds for the spectral radius of positive operators

Roman Drnovšek

Displaying similar documents to “Bounds for the spectral radius of positive operators”

On the spectral multiplicity of a direct sum of operators

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 $l^{p}$ and a suitable bounded linear operator A on a Banach space X.

On the joint spectral radius

Vladimír Müller (1997)

Annales Polonici Mathematici

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

Formulae for joint spectral radii of sets of operators

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

Studia Mathematica

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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.

About the decision of reachability for register machines

Véronique Cortier (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We study the decidability of the following problem: given $p$ affine functions $f_{1}, ..., f_{p}$ over $ℕ^{k}$ and two vectors $v_{1}, v_{2} \in ℕ^{k}$ , is $v_{2}$ reachable from $v_{1}$ by successive iterations of $f_{1}, ..., f_{p}$ (in this given order)? We show that this question is decidable for $p = 1, 2$ and undecidable for some fixed $p$ .

Multipliers and Wiener-Hopf operators on weighted L p spaces

Violeta Petkova (2013)

Open Mathematics

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We study multipliers M (bounded operators commuting with translations) on weighted spaces L ω p (ℝ), and establish the existence of a symbol µM for M, and some spectral results for translations S t and multipliers. We also study operators T on the weighted space L ω p (ℝ+) commuting either with the right translations S t , t ∈ ℝ+, or left translations P +S −t , t ∈ ℝ+, and establish the existence of a symbol µ of T. We characterize completely the spectrum σ(S t ) of the operator S t...

On the spectral radius of positive operators.

C.D. Aliprantis, Y.A. Abramovich (1992)

Mathematische Zeitschrift

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

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 $C_{A}$ to the isospectral variety at A. In the case of Ω₃, the zero set of the Kobayashi-Royden pseudometric is completely described.

On the spectral radius of positive operators (Corrigendum).

C.D. Aliprantis, Y.A. Abramovich (1994)

Mathematische Zeitschrift

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A spectral gap property for subgroups of finite covolume in Lie groups

Bachir Bekka, Yves Cornulier (2010)

Colloquium Mathematicae

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Let G be a real Lie group and H a lattice or, more generally, a closed subgroup of finite covolume in G. We show that the unitary representation $λ_{G / H}$ of G on L²(G/H) has a spectral gap, that is, the restriction of $λ_{G / H}$ to the orthogonal complement of the constants in L²(G/H) does not have almost invariant vectors. This answers a question of G. Margulis. We give an application to the spectral geometry of locally symmetric Riemannian spaces of infinite volume.

Quotient of spectral radius, (signless) Laplacian spectral radius and clique number of graphs

Kinkar Ch. Das, Muhuo Liu (2016)

Czechoslovak Mathematical Journal

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In this paper, the upper and lower bounds for the quotient of spectral radius (Laplacian spectral radius, signless Laplacian spectral radius) and the clique number together with the corresponding extremal graphs in the class of connected graphs with $n$ vertices and clique number $ω$ $(2 \leq ω \leq n)$ are determined. As a consequence of our results, two conjectures given in Aouchiche (2006) and Hansen (2010) are proved.

Spectral mapping inclusions for the Phillips functional calculus in Banach spaces and algebras

Eva Fašangová, Pedro J. Miana (2005)

Studia Mathematica

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We investigate the weak spectral mapping property (WSMP) $\bar{μ ̂ (σ (A))} = σ (μ ̂ (A))$ , where A is the generator of a ₀-semigroup in a Banach space X, μ is a measure, and μ̂(A) is defined by the Phillips functional calculus. We consider the special case when X is a Banach algebra and the operators $e^{A t}$ , t ≥ 0, are multipliers.

Spectral sets and the Drazin inverse with applications to second order differential equations

Trung Dinh Tran (2002)

Applications of Mathematics

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The paper defines and studies the Drazin inverse for a closed linear operator $A$ in a Banach space $X$ in the case that $0$ belongs to a spectral set of the spectrum of $A$ . Results are applied to extend a result of Krein on a nonhomogeneous second order differential equation in a Banach space.