@article{Vasylyshyn_Zahorodniuk_2022, title={Weakly symmetric functions on spaces of Lebesgue integrable functions}, volume={14}, url={https://scijournals.pnu.edu.ua/index.php/cmp/article/view/6476}, DOI={10.15330/cmp.14.2.437-441}, abstractNote={<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>}, number={2}, journal={Carpathian Mathematical Publications}, author={VasylyshynT.V. and ZahorodniukV.A.}, year={2022}, month={Dec.}, pages={437-441} }