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Notes about the Hypercyclicity Criterion

In: Mathematica Slovaca, vol. 53, no. 3
Fernando León-Saavedra
Detaily:
Rok, strany: 2003, 313 - 319
O článku:
A Banach space operator $T$ is said to be hypercyclic if there exists a vector $x$ such that the orbit $\{Tnx\}$ is dense in the space. The most used tool to discover hypercyclic operators is known as the Hypercyclicity Criterion. Given an operator $T$ satisfying the Hypercyclicity Criterion, we characterize the subsequences of natural numbers $\{nk\}$ for which we can assert that the sequence of powers $\{Tnk\}$ also satisfies it. In order to show that, some equivalent conditions of the Hypercyclicity Criterion are studied. Finally as a consequence of this analysis we show that hypercyclic operators with a dense subset of almost periodic vectors satisfy the Hypercyclicity Criterion.
Ako citovať:
ISO 690:
León-Saavedra, F. 2003. Notes about the Hypercyclicity Criterion. In Mathematica Slovaca, vol. 53, no.3, pp. 313-319. 0139-9918.

APA:
León-Saavedra, F. (2003). Notes about the Hypercyclicity Criterion. Mathematica Slovaca, 53(3), 313-319. 0139-9918.