On a weak Freudenthal spectral theorem
Commentationes Mathematicae Universitatis Carolinae (1992)
- Volume: 33, Issue: 4, page 631-643
- ISSN: 0010-2628
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topWójtowicz, Marek. "On a weak Freudenthal spectral theorem." Commentationes Mathematicae Universitatis Carolinae 33.4 (1992): 631-643. <http://eudml.org/doc/247388>.
@article{Wójtowicz1992,
abstract = {Let $X$ be an Archimedean Riesz space and $\Cal P(X)$ its Boolean algebra of all band projections, and put $\Cal P_\{e\}=\\{P e:P\in \Cal P(X)\\}$ and $\Cal B_\{e\}=\\{x\in X: x\wedge (e-x)=0\\}$, $e\in X^+$. $X$ is said to have Weak Freudenthal Property (\text\{$\operatorname\{WFP\}$\}) provided that for every $e\in X^+$ the lattice $lin\, \Cal P_\{e\}$ is order dense in the principal band $e^\{d d\}$. This notion is compared with strong and weak forms of Freudenthal spectral theorem in Archimedean Riesz spaces, studied by Veksler and Lavrič, respectively. \text\{$\operatorname\{WFP\}$\} is equivalent to $X^+$-denseness of $\Cal P_\{e\}$ in $\Cal B_\{e\}$ for every $e\in X^+$, and every Riesz space with sufficiently many projections has \text\{$\operatorname\{WFP\}$\} (THEOREM).},
author = {Wójtowicz, Marek},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {disjointness; Archimedean Riesz space; Boolean algebra of all band projections; weak Freudenthal property; strong and weak forms of Freudenthal spectral theorem},
language = {eng},
number = {4},
pages = {631-643},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a weak Freudenthal spectral theorem},
url = {http://eudml.org/doc/247388},
volume = {33},
year = {1992},
}
TY - JOUR
AU - Wójtowicz, Marek
TI - On a weak Freudenthal spectral theorem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 4
SP - 631
EP - 643
AB - Let $X$ be an Archimedean Riesz space and $\Cal P(X)$ its Boolean algebra of all band projections, and put $\Cal P_{e}=\{P e:P\in \Cal P(X)\}$ and $\Cal B_{e}=\{x\in X: x\wedge (e-x)=0\}$, $e\in X^+$. $X$ is said to have Weak Freudenthal Property (\text{$\operatorname{WFP}$}) provided that for every $e\in X^+$ the lattice $lin\, \Cal P_{e}$ is order dense in the principal band $e^{d d}$. This notion is compared with strong and weak forms of Freudenthal spectral theorem in Archimedean Riesz spaces, studied by Veksler and Lavrič, respectively. \text{$\operatorname{WFP}$} is equivalent to $X^+$-denseness of $\Cal P_{e}$ in $\Cal B_{e}$ for every $e\in X^+$, and every Riesz space with sufficiently many projections has \text{$\operatorname{WFP}$} (THEOREM).
LA - eng
KW - disjointness; Archimedean Riesz space; Boolean algebra of all band projections; weak Freudenthal property; strong and weak forms of Freudenthal spectral theorem
UR - http://eudml.org/doc/247388
ER -
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