@article{LAVRIČ_1990, title={ A NOTE ON LATTICE OPERATIONS OF RIESZ SPACES OF ORDER BOUNDED OPERATORS}, volume={21}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4688}, DOI={10.5556/j.tkjm.21.1990.4688}, abstractNote={<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">Let $</span><span style="font-size: 10.000000pt; font-family: ’Arial’; font-style: italic;">L$, $M$ </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">be Archimedean Riesz spaces with $</span><span style="font-size: 10.000000pt; font-family: ’Arial’; font-style: italic;">M$ </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">Dedekind complete, and let $\mathcal L_</span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">b(L,M )$ </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">be the Riesz space of order bounded linear operators from $</span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">L$ </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">into $</span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">M$. </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">A theorem of Abramovic [1] on lattice operations of </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">$\mathcal L_</span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">b(L,M )$ </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">is generalized on Riesz spaces $</span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">L$ in </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">which a weak form of Freudenthal’s spectral theorem [4] holds. </span></p> </div> </div> </div>}, number={4}, journal={Tamkang Journal of Mathematics}, author={LAVRIČ, BORIS}, year={1990}, month={Dec.}, pages={395–398} }