Bounded semigroups of matrices
نویسندگان
چکیده
منابع مشابه
Bounded Semigroups of Matrices
In this note are proved two conjectures of Daubechies and Lagarias. The first asserts that if Z is a bounded set of matrices such that all left infinite products converge, then 8 generates a bounded semigroup. The second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices. One definition involves the conventional spectral radius, and one involves t...
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It is proved that for polynomially bounded sets of matrices the notions of pointwise convergence and uniform convergence coincide. This result is also proved for certain sets of nonlinear maps on finite-dimensional real or complex vector spaces.
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We characterize generators of polynomially bounded C0-semigroups in terms of an integrability condition for the second power of the resolvent on vertical lines. This generalizes results by Gomilko, Shi and Feng on bounded semigroups and by Malejki on polynomially bounded groups.
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The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...
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54 M.Mijatović, S.Pilipović 0. Introduction One-time integrated and n-times integrated exponentially bounded semigroups (n-t.i.e.b.s., in short), n ∈ N, of operators on a Banach space introduced by Arendt, were developed in [1-2], [13-16], [19], [22], [29-30] and applied to abstract Cauchy problems with operators which do not generate C0-semigroups. More generally, α-times integrated semigroups...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1992
ISSN: 0024-3795
DOI: 10.1016/0024-3795(92)90267-e