Let $E$ be a smooth, strictly convex and reflexive Banach space, let $Y^*$ be a closed linear subspace of the dual space $E^*$ of $E$ and let $\Pi_{Y^*}$ be the generalized projection of $E^*$ onto $Y^*$. Then, the mapping $E_{Y^*}$ of $E$ into $E$ defined by $E_{Y^*}=J^{-1}\Pi_{Y^*}J$ is called the generalized conditional expectation with respect to $Y^*$, where $J$ is the normalized duality mapping from $E$ into $E^*$. In this paper, we prove two results which are related to norm one linear projections and generalized conditional expectations in Banach spaces.