TY - JOUR AU - LAVRIČ, BORIS PY - 1990/12/01 Y2 - 2024/03/28 TI - A NOTE ON LATTICE OPERATIONS OF RIESZ SPACES OF ORDER BOUNDED OPERATORS JF - Tamkang Journal of Mathematics JA - Tamkang J. Math. VL - 21 IS - 4 SE - Papers DO - 10.5556/j.tkjm.21.1990.4688 UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4688 SP - 395-398 AB - <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> ER -