Co-analytic, right-invertible operators are supercyclic

Sameer Chavan

Sameer Chavan

Colloquium Mathematicae, Tome 120 (2010), p. 137-142 / Harvested from The Polish Digital Mathematics Library

Résumé

Let denote a complex, infinite-dimensional, separable Hilbert space, and for any such Hilbert space , let () denote the algebra of bounded linear operators on . We show that for any co-analytic, right-invertible T in (), αT is hypercyclic for every complex α with $| α | > β^{- 1}$ , where $β \equiv i n f_{| | x | | = 1} | | T * x | | > 0$ . In particular, every co-analytic, right-invertible T in () is supercyclic.

Publié le : 2010-01-01

Zbl 1206.47010

EUDML-ID : urn:eudml:doc:283801

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     title = {Co-analytic, right-invertible operators are supercyclic},
     journal = {Colloquium Mathematicae},
     volume = {120},
     year = {2010},
     pages = {137-142},
     zbl = {1206.47010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-9}
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Sameer Chavan. Co-analytic, right-invertible operators are supercyclic. Colloquium Mathematicae, Tome 120 (2010) pp. 137-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-9/