an:01356620
Zbl 0940.47005
Salas, H??ctor N.
Supercyclicity and weighted shifts
EN
Stud. Math. 135, No. 1, 55-74 (1999).
00055914
1999
j
47A16 47A65
cyclicity; hypercyclicity; supercyclicity; Fr??chet spaces; supercyclic bilateral shifts; weight sequences; \(C^*\)-isomorphisms
After introducing the notion of cyclicity, hypercyclicity and supercyclicity the author presents a sufficient criterion for supercyclicity in Fr??chet spaces along with some of its consequences. These results are used for characterizing the supercyclic bilateral shifts in terms of their weight sequences.
If the operators in question act on a separable Hilbert space one can ask whether hypercyclicity is preserved under \(C^*\)-isomorphisms. This question is answered negatively, even when the operators in question are supercyclic.
It is proved that a Banach space operator \(T\) has an infinite-dimensional closed subspace whose non-zero vectors are supercyclic, provided that \(T\) satisfies a supercyclicity criterion and zero is in its left essential spectrum. The paper ends with some concluding remarks and open questions.
Andr?? Noll (Clausthal-Zellerfeld)