On a weak Freudenthal spectral theorem
Wójtowicz, Marek
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 631-643 / Harvested from Czech Digital Mathematics Library
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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).

Publié le : 1992-01-01
Classification:  06B10,  06E99,  46A40 
@article{118535,
     author = {Marek W\'ojtowicz},
     title = {On a weak Freudenthal spectral theorem},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {631-643},
     zbl = {0777.46006},
     mrnumber = {1240185},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118535}
}

Wójtowicz, Marek. On a weak Freudenthal spectral theorem. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 631-643. http://gdmltest.u-ga.fr/item/118535/

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