Weakly symmetric functions on spaces of Lebesgue integrable functions

In this work, we present the notion of a weakly symmetric function. We show that subset all elements an arbitrary vector space functions is itself. Moreover, some algebra algebra. Also consider on complex Banach $L_p[0,1]$ Lebesgue measurable complex-valued $[0,1]$ for which $p$th power absolute value integrable. every continuous linear functional $L_p[0,1],$ where $p\in (1,+\infty),$ can be approximated by functionals.