TY - JOUR
AU - Vasylyshyn, T.V.
AU - Zahorodniuk, V.A.
PY - 2022/12/30
Y2 - 2024/06/18
TI - Weakly symmetric functions on spaces of Lebesgue integrable functions
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 14
IS - 2
SE - Scientific articles
DO - 10.15330/cmp.14.2.437-441
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/6476
SP - 437-441
AB - <p>In this work, we present the notion of a weakly symmetric function. We show that the subset of all weakly symmetric elements of an arbitrary vector space of functions is a vector space. Moreover, the subset of all weakly symmetric elements of some algebra of functions is an algebra. Also we consider weakly symmetric functions on the complex Banach space $L_p[0,1]$ of all Lebesgue measurable complex-valued functions on $[0,1]$ for which the $p$th power of the absolute value is Lebesgue integrable. We show that every continuous linear functional on $L_p[0,1],$ where $p\in (1,+\infty),$ can be approximated by weakly symmetric continuous linear functionals.</p>
ER -