Let's suppose we have a Hilbert space $\mathcal{H}$ and the C*-algebra of the set of bounded operators $\mathcal{B}(\mathcal{H})$. For what I have understood, unbounded operators as for example position $\hat{x}$ and momentum $\hat{p}$ operators enter in the algebra $\mathcal{B}(\mathcal{H})$ as generators of strongly continuous group of unitary operators. Can we say that the projectors into the eigenstates of $\hat{x}$ and $\hat{p}$ are in $\mathcal{B}(\mathcal{H})$?

Let's suppose we have a Hilbert space $\mathcal{H}$ and the C*-algebra of the set of bounded operators $\mathcal{B}(\mathcal{H})$. For what I have understood, unbounded operators as for example position $\hat{x}$ and momentum $\hat{p}$ operators enter in the algebra $\mathcal{B}(\mathcal{H})$ as generators of strongly continuous group of unitary operators. Can we say that the projectors into the eigenstates of $\hat{x}$ and $\hat{p}$ are in $\mathcal{B}(\mathcal{H})$?

Edit

For eigenstates of $\hat{x}$ and $\hat{p}$ I mean here the vectors that approximate as close as you want to eigenstates of the unbounded operators