On submultiplicativity of spectral radius and transitivity of semigroups |
| |
| Authors: | Heydar Radjavi Peter Rosenthal |
| |
| Institution: | Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 ; Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3 |
| |
| Abstract: | It is shown that a transitive, closed, homogeneous semigroup of linear transformations on a finite-dimensional space either has zero divisors or is simultaneously similar to a group consisting of scalar multiples of unitary transformations. The proof begins with the result that for each closed homogeneous semigroup with no zero divisors there is a  such that the spectral radius satisfies  for all  and  in the semigroup. It is also shown that the spectral radius is not  -submultiplicative on any transitive semigroup of compact operators. |
| |
| Keywords: | |
|
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 |
| 点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文 |
|
