caa a22 4500 467931577 CHVBK 20180406152945.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s00020-005-1394-0 doi (NATIONALLICENCE)springer-10.1007/s00020-005-1394-0 Weak* Hypercyclicity and Supercyclicity of Shifts on ℓ∞ [Elektronische Daten] [Juan Bès, Kit Chan, Rebecca Sanders] Abstract.: We study hypercyclicity and supercyclicity of weighted shifts on ℓ∞, with respect to the weak * topology. We show that there exist bilateral shifts that are weak * hypercyclic but fail to be weak * sequentially hypercyclic. In the unilateral case, a shift T is weak * hypercyclic if and only if it is weak * sequentially hypercyclic, and this is equivalent to T being either norm, weak, or weak-sequentially hypercyclic on c0 or ℓp(1≤p<∞). We also show that the set of weak * hypercyclic vectors of any unilateral or bilateral shift on ℓ∞ is norm nowhere dense. Finally, we show that ℓ∞ supports an isometry that is weak * sequentially supercyclic. Birkhäuser Verlag, Basel, 2006 Weak topology nationallicence weak * topology nationallicence norm topology nationallicence hypercyclic vectors nationallicence hypercyclic operators nationallicence sequence spaces nationallicence Bès Juan Department of Mathematics and Statistics, Bowling Green State University, 43403, Bowling Green, Ohio, USA aut Chan Kit Department of Mathematics and Statistics, Bowling Green State University, 43403, Bowling Green, Ohio, USA aut Sanders Rebecca Department of Mathematics, Statistics and Computer Sciences, Marquette University, 53201, Milwaukee, Wisconsin, USA aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 55/3(2006-07-01), 363-376 0378-620X 55:3<363 2006 55 20 https://doi.org/10.1007/s00020-005-1394-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-005-1394-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bès Juan Department of Mathematics and Statistics, Bowling Green State University, 43403, Bowling Green, Ohio, USA aut NATIONALLICENCE 700 1- Chan Kit Department of Mathematics and Statistics, Bowling Green State University, 43403, Bowling Green, Ohio, USA aut NATIONALLICENCE 700 1- Sanders Rebecca Department of Mathematics, Statistics and Computer Sciences, Marquette University, 53201, Milwaukee, Wisconsin, USA aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 55/3(2006-07-01), 363-376 0378-620X 55:3<363 2006 55 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer