Displaying similar documents to “Asymptotic stability of linear differential equations in Banach spaces”

A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum

Charles Batty, Zdzisław Brzeźniak, David Greenfield (1996)

Studia Mathematica

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Let T be a semigroup of linear contractions on a Banach space X, and let X s ( T ) = x ∈ X : l i m s → ∞ ∥ T ( s ) x ∥ = 0 . Then X s ( T ) is the annihilator of the bounded trajectories of T*. If the unitary spectrum of T is countable, then X s ( T ) is the annihilator of the unitary eigenvectors of T*, and l i m s ∥ T ( s ) x ∥ = i n f ∥ x - y ∥ : y ∈ X s ( T ) for each x in X.

Almost periodic and strongly stable semigroups of operators

Vũ Phóng (1997)

Banach Center Publications

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This paper is chiefly a survey of results obtained in recent years on the asymptotic behaviour of semigroups of bounded linear operators on a Banach space. From our general point of view, discrete families of operators T n : n = 0 , 1 , . . . on a Banach space X (discrete one-parameter semigroups), one-parameter C 0 -semigroups T ( t ) : t ≥ 0 on X (strongly continuous one-parameter semigroups), are particular cases of representations of topological abelian semigroups. Namely, given a topological abelian semigroup S, a family...

Relation between the boundary point spectrum of a generator and of its adjoint.

Fuensanta Andreu Vaíllo, José Manuel Mazón Ruiz (1990)

Publicacions Matemàtiques

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In this paper we get some relations between the boundary point spectrum of the generator A of a C-semigroup and the generator A* of the dual semigroup. This relations combined with the results due to Lyubich-Phong and Arendt-Batty, yield stability results on positive C-semigroups.