Determining if $L$ = {$ { a^nsb^n : s \in L(a^*b^*) ,\ n \ge 1 } $} is not a regular language using Pumping Lemma? In short, is this similar to how $a^nb^n$ is not a regular langauge?

$L$ = {$ { a^nsb^n : s \in L(a^*b^*) ,\ n \ge 1 } $}

For instance, if we have the string  $w=a^psb^p$, and we know that $|xy| \le p$, there would simply be a disproportianate amount of a's or b's regardless of where we put $y$ ?
Your language is equal to $L(a^+b^+)$ (why?).