Asymptotics of Semigroups Generated by Operator Matrices
نویسنده
چکیده
We survey some known results about generator property of operator matrices with diagonal or coupled domain. Further, we use basic properties of the convolution of operator-valued mappings in order to obtain stability results for such semigroups. 1. Operator matrices with diagonal domain While tackling abstract problems that are related to concrete initial–boundary value problems with dynamical boundary conditions and/or with coupled systems of PDE’s, it is common that one has to check whether an operator matrix (1.1) A := (
منابع مشابه
Semigroups of matrices with dense orbits
We prove that for any n ≥ 1 there exist n × n matrices A and B such that for any vector x ∈ R with a nonzero first component, the orbit of x under the action of the semigroup generated by A and B is dense in R. As a corollary, we prove that for a large set of diagonal matrices A and B and any vector V with nonzero entries, the orbit of any vector under the semigroup generated by the affine maps...
متن کامل5 Arnold ’ s Conjectures on Weak Asymptotics and Statistics of Numerical
Three conjectures #1999–8, #1999–9 and #1999–10 which were posed by V. Arnold [2] and devoted to the statistics of the numerical semigroups are refuted for the case of semigroups generated by three positive integers d 1 , d 2 , d 3 with gcd(d 1 , d 2 , d 3) = 1. Weak asymptotics of conductor C(d 1 , d 2 , d 3) of numerical semigroup and fraction p(d 1 , d 2 , d 3) of a segment [0; C(d 1 , d 2 ,...
متن کاملFurther inequalities for operator space numerical radius on 2*2 operator matrices
We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$, when $X$ is a numerical radius operator space. These inequalities contain some upper and lower bounds for operator space numerical radius.
متن کاملSemigroup of matrices acting on the max-plus projective space
We investigate the action of semigroups of d× d matrices with entries in the max-plus semifield on the max-plus projective space. Recall that semigroups generated by one element with projectively bounded image are projectively finite and thus contain idempotent elements. In terms of orbits, our main result states that the image of a minimal orbit by an idempotent element of the semigroup with m...
متن کاملYet Another Solution to the Burnside Problem for Matrix Semigroups
We use the kernel category to give a finiteness condition for semigroups. As a consequence we provide yet another proof that finitely generated periodic semigroups of matrices are finite.
متن کامل