Unicellularity of the multiplication operator on Banach spaces of formal power series

@article{B2001,
abstract = {Let $\{β(n)\}^\{∞\}_\{n=0\}$ be a sequence of positive numbers and 1 ≤ p < ∞. We consider the space $ℓ^\{p\}(β)$ of all power series $f(z) = ∑^\{∞\}_\{n=0\} f̂(n)zⁿ$ such that $∑_\{n=0\}^\{∞\} |f̂(n)|^\{p\}|β(n)|^\{p\} < ∞$. We give some sufficient conditions for the multiplication operator, $M_\{z\}$, to be unicellular on the Banach space $ℓ^\{p\}(β)$. This generalizes the main results obtained by Lu Fang [1].},
author = {B. Yousefi},
journal = {Studia Mathematica},
keywords = {invariant subspace lattice; Banach space of formal power series; cyclic vector; unicellular operator; shift operator; weighted space},
language = {eng},
number = {3},
pages = {201-209},
title = {Unicellularity of the multiplication operator on Banach spaces of formal power series},
url = {http://eudml.org/doc/286211},
volume = {147},
year = {2001},
}

TY - JOUR
AU - B. Yousefi
TI - Unicellularity of the multiplication operator on Banach spaces of formal power series
JO - Studia Mathematica
PY - 2001
VL - 147
IS - 3
SP - 201
EP - 209
AB - Let ${β(n)}^{∞}_{n=0}$ be a sequence of positive numbers and 1 ≤ p < ∞. We consider the space $ℓ^{p}(β)$ of all power series $f(z) = ∑^{∞}_{n=0} f̂(n)zⁿ$ such that $∑_{n=0}^{∞} |f̂(n)|^{p}|β(n)|^{p} < ∞$. We give some sufficient conditions for the multiplication operator, $M_{z}$, to be unicellular on the Banach space $ℓ^{p}(β)$. This generalizes the main results obtained by Lu Fang [1].
LA - eng
KW - invariant subspace lattice; Banach space of formal power series; cyclic vector; unicellular operator; shift operator; weighted space
UR - http://eudml.org/doc/286211
ER -