In this work, we study the shrinkage estimator (the James-Stein estimators) of the mean of a Gaussian distribution in a Hilbert space of infinite dimensional, then we take a variable  in the Hilbert space  defined by its inner product    and propose some forms of the shrinkage estimators, that we show which are better under quadratic risk than the empirical estimator X.

quadratic loss function, quadratic risk, shrinkage estimators, Hilbert space.