# Positivity in the theory of supercyclic operators

F. León-Saavedra; A. Piqueras-Lerena

Banach Center Publications (2007)

- Volume: 75, Issue: 1, page 221-232
- ISSN: 0137-6934

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topF. León-Saavedra, and A. Piqueras-Lerena. "Positivity in the theory of supercyclic operators." Banach Center Publications 75.1 (2007): 221-232. <http://eudml.org/doc/282404>.

@article{F2007,

abstract = {A bounded linear operator T defined on a Banach space X is said to be supercyclic if there exists a vector x ∈ X such that the projective orbit \{λTⁿx : λ ∈ ℂ, n ∈ ℕ\} is dense in X. The aim of this survey is to show the relationship between positivity and supercyclicity. This relationship comes from the so called Positive Supercyclicity Theorem. Throughout this exposition, interesting new directions and open problems will appear.},

author = {F. León-Saavedra, A. Piqueras-Lerena},

journal = {Banach Center Publications},

keywords = {supercyclic vectors; positivity; invariant subspaces},

language = {eng},

number = {1},

pages = {221-232},

title = {Positivity in the theory of supercyclic operators},

url = {http://eudml.org/doc/282404},

volume = {75},

year = {2007},

}

TY - JOUR

AU - F. León-Saavedra

AU - A. Piqueras-Lerena

TI - Positivity in the theory of supercyclic operators

JO - Banach Center Publications

PY - 2007

VL - 75

IS - 1

SP - 221

EP - 232

AB - A bounded linear operator T defined on a Banach space X is said to be supercyclic if there exists a vector x ∈ X such that the projective orbit {λTⁿx : λ ∈ ℂ, n ∈ ℕ} is dense in X. The aim of this survey is to show the relationship between positivity and supercyclicity. This relationship comes from the so called Positive Supercyclicity Theorem. Throughout this exposition, interesting new directions and open problems will appear.

LA - eng

KW - supercyclic vectors; positivity; invariant subspaces

UR - http://eudml.org/doc/282404

ER -

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