  In this Letter we present a calculation of the one-particle irreducible
density matrix $\rho(x)$ for the one-dimensional (1D) Hubbard model in the
infinite $U$ limit. We consider the zero temperature spin disordered regime,
which is obtained by first taking the limit $U\to \infty$ and then the limit
$T\to 0.$ Using the determinant representation for $\rho(x)$ we derive
analytical expressions for both large and small $x$ at an arbitrary filling
factor $0<\varrho<1/2.$ The large $x$ asymptotics of $\rho(x)$ is found to be
remarkably accurate starting from $x\sin(2\pi\varrho)\sim 1.$ We find that the
one-particle momentum distribution function $\rho(k)$ is a smooth function of
$k$ peaked at $k=2k_F,$ thus violating the Luttinger theorem.
