- Tytuł:
- Supercyclicity and weighted shifts
- Autorzy:
- Salas, Héctor N.
- Powiązania:
- https://bibliotekanauki.pl/articles/1217170.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
hypercyclic and supercyclic vectors
Hypercyclicity Criterion
Supercyclicity Criterion
weighted shifts
semi-Fredholm operators in Banach spaces
left essential spectrum
basic sequences. - Opis:
- An operator (linear and continuous) in a Fréchet space is hypercyclic if there exists a vector whose orbit under the operator is dense. If the scalar multiples of the elements in the orbit are dense, the operator is supercyclic. We give, for Fréchet space operators, a Supercyclicity Criterion reminiscent of the Hypercyclicity Criterion. We characterize the supercyclic bilateral weighted shifts in terms of their weight sequences. As a consequence, we show that a bilateral weighted shift is supercyclic if and only if it satisfies the Supercyclicity Criterion. We exhibit two supercyclic, irreducible Hilbert space operators which are C*-isomorphic, but one is hypercyclic and the other is not. We prove that a Banach space operator which satisfies a version of the Supercyclicity Criterion, and has zero in its left essential spectrum, has an infinite-dimensional closed subspace whose nonzero vectors are supercyclic.
- Źródło:
-
Studia Mathematica; 1999, 135, 1; 55-74
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł