# Bounds for the spectral radius of positive operators

Commentationes Mathematicae Universitatis Carolinae (2000)

- Volume: 41, Issue: 3, page 459-467
- ISSN: 0010-2628

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topDrnovšek, Roman. "Bounds for the spectral radius of positive operators." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 459-467. <http://eudml.org/doc/248602>.

@article{Drnovšek2000,

abstract = {Let $f$ be a non-zero positive vector of a Banach lattice $L$, and let $T$ be a positive linear operator on $L$ with the spectral radius $r(T)$. We find some groups of assumptions on $L$, $T$ and $f$ under which the inequalities \[ \sup \lbrace c \ge 0 : T f \ge c \, f\rbrace \le r(T) \le \inf \lbrace c \ge 0 : T f \le c \, f\rbrace \]
hold. An application of our results gives simple upper and lower bounds for the spectral radius of a product of positive operators in terms of positive eigenvectors corresponding to the spectral radii of given operators. We thus extend the matrix result obtained by Johnson and Bru which was the motivation for this paper.},

author = {Drnovšek, Roman},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Banach lattices; positive operators; spectral radius; Banach lattice; positive operator; spectral radius; Collatz-Wielandt bounds},

language = {eng},

number = {3},

pages = {459-467},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Bounds for the spectral radius of positive operators},

url = {http://eudml.org/doc/248602},

volume = {41},

year = {2000},

}

TY - JOUR

AU - Drnovšek, Roman

TI - Bounds for the spectral radius of positive operators

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2000

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 41

IS - 3

SP - 459

EP - 467

AB - Let $f$ be a non-zero positive vector of a Banach lattice $L$, and let $T$ be a positive linear operator on $L$ with the spectral radius $r(T)$. We find some groups of assumptions on $L$, $T$ and $f$ under which the inequalities \[ \sup \lbrace c \ge 0 : T f \ge c \, f\rbrace \le r(T) \le \inf \lbrace c \ge 0 : T f \le c \, f\rbrace \]
hold. An application of our results gives simple upper and lower bounds for the spectral radius of a product of positive operators in terms of positive eigenvectors corresponding to the spectral radii of given operators. We thus extend the matrix result obtained by Johnson and Bru which was the motivation for this paper.

LA - eng

KW - Banach lattices; positive operators; spectral radius; Banach lattice; positive operator; spectral radius; Collatz-Wielandt bounds

UR - http://eudml.org/doc/248602

ER -

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