The Unitary Equivalence Of Quasi-invariant

In this paper, we mainly deal with the unitary equivalence of two quasi-invariant subspaces generated by polynomial ideal. If one is unitary equivalent to the other if and only if they equals. Because we deal with things in the primise that polynomial ideal is quasi-invariant subspaces of X. We have some examples that polynomial ideal is quasi-invariant subspaces in the primise of the special condition. But we have to study more for the generality. After that, we show that two quasi-invariant subspaces of X have the unitary equivalence if and only if they equals. At last, we show the unitary equivalence of two quasi-invariant subspaces generated by polynomial ideal is unitary equivalent to the other if and only if they equals.