Power bounded and exponentially bounded matrices

A note on power bounded matrices

Ela a Note on Power Bounded Matrices

We say A is convergent to the matrix X = [xij ] if the sequences (A )ij converge to xij as k → ∞. A matrix is convergent if it is convergent to some matrix. This is a special case of convergence as defined in [4, Definition 10.1], for the matrix sequence {A,A, A, . . . }. In particular, we say A is zero convergent when A is convergent to the zero matrix. We distinguish between convergence and z...

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

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 ...

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...

A Class of Exponentially Bounded Distribution Semigroups

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...