On weak supercyclicity II

Carlos S. Kubrusly; Bhagwati P. Duggal

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 2, page 371-386
  • ISSN: 0011-4642

Abstract

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This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators: (i) self-adjoint operators are not weakly supercyclic, (ii) diagonalizable operators are not weakly l -sequentially supercyclic, and (iii) weak l -sequential supercyclicity is preserved between a unitary operator and its adjoint. On the other hand, weak supercyclicity is investigated for classes of normed-space operators: (iv) the point spectrum of the normed-space adjoint of a power bounded supercyclic operator is either empty or is a singleton in the open unit disk, (v) weak l -sequential supercyclicity coincides with supercyclicity for compact operators, and (vi) every compact weakly l -sequentially supercyclic operator is quasinilpotent.

How to cite

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Kubrusly, Carlos S., and Duggal, Bhagwati P.. "On weak supercyclicity II." Czechoslovak Mathematical Journal 68.2 (2018): 371-386. <http://eudml.org/doc/294485>.

@article{Kubrusly2018,
abstract = {This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators: (i) self-adjoint operators are not weakly supercyclic, (ii) diagonalizable operators are not weakly $l$-sequentially supercyclic, and (iii) weak $l$-sequential supercyclicity is preserved between a unitary operator and its adjoint. On the other hand, weak supercyclicity is investigated for classes of normed-space operators: (iv) the point spectrum of the normed-space adjoint of a power bounded supercyclic operator is either empty or is a singleton in the open unit disk, (v) weak $l$-sequential supercyclicity coincides with supercyclicity for compact operators, and (vi) every compact weakly $l$-sequentially supercyclic operator is quasinilpotent.},
author = {Kubrusly, Carlos S., Duggal, Bhagwati P.},
journal = {Czechoslovak Mathematical Journal},
keywords = {supercyclic operator; weakly supercyclic operator; weakly $l$-sequentially supercyclic operator},
language = {eng},
number = {2},
pages = {371-386},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On weak supercyclicity II},
url = {http://eudml.org/doc/294485},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Kubrusly, Carlos S.
AU - Duggal, Bhagwati P.
TI - On weak supercyclicity II
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 2
SP - 371
EP - 386
AB - This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators: (i) self-adjoint operators are not weakly supercyclic, (ii) diagonalizable operators are not weakly $l$-sequentially supercyclic, and (iii) weak $l$-sequential supercyclicity is preserved between a unitary operator and its adjoint. On the other hand, weak supercyclicity is investigated for classes of normed-space operators: (iv) the point spectrum of the normed-space adjoint of a power bounded supercyclic operator is either empty or is a singleton in the open unit disk, (v) weak $l$-sequential supercyclicity coincides with supercyclicity for compact operators, and (vi) every compact weakly $l$-sequentially supercyclic operator is quasinilpotent.
LA - eng
KW - supercyclic operator; weakly supercyclic operator; weakly $l$-sequentially supercyclic operator
UR - http://eudml.org/doc/294485
ER -

References

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