Convergence of Polynomially Bounded Semigroups of Matrices
نویسندگان
چکیده
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.
منابع مشابه
Polynomially bounded C0-semigroups
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.
متن کاملPolynomially bounded solutions of the Loewner differential equation in several complex variables
We determine the form of polynomially bounded solutions to the Loewner differential equation that is satisfied by univalent subordination chains of the form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$, where $A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally Lebesgue integrable mapping and satisfying the condition $$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t [A(tau)...
متن کاملComplex Powers of Nondensely Defined Operators
The power (−A)b, b ∈ C is defined for a closed linear operator A whose resolvent is polynomially bounded on the region which is, in general, strictly contained in an acute angle. It is proved that all structural properties of complex powers of densely defined operators with polynomially bounded resolvent remain true in the newly arisen situation. The fractional powers are considered as generato...
متن کاملDecomposition of H*-Algebra Valued Negative Definite Functions on Topological *-Semigroups
In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author ...
متن کاملA 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 ...
متن کامل