Abstract
Let $E$ be a smooth, strictly convex and reflexive Banach space, let $C_*$ be a closed linear subspace of the dual space $E^*$ of $E$ and let $\Pi_{C_*}$ be the generalized projection of $E^*$ onto $C_*$. In this paper, we study the mapping $R$ defined by $R = J^{-1} \Pi_{C_*}J$, where $J$ is the normalized duality mapping from $E$ into $E^*$. We obtain some results which are related to conditional expectations and martingales in the probability theory.
Citation
Takashi Honda. Wataru Takahashi. "NONLINEAR PROJECTIONS AND GENERALIZED CONDITIONAL EXPECTATIONS IN BANACH SPACES." Taiwanese J. Math. 15 (5) 2169 - 2193, 2011. https://doi.org/10.11650/twjm/1500406429
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