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Let ℒ($H$) denote the space of operators on a Hilbert space$H$. We show that the extreme points of the unit ball of the space of continuous functions$C(K, ℒ(H))$($K$-compact Hausdorff) are precisely the functions with extremal values. We show also that these extreme points are (a) strongly exposed if and only if dim$H$<∞ and card$K$<∞, (b) exposed if and only if$H$is separable and$K$carries a strictly positive measure.

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The multiple testing procedure plays an important role in detecting the presence of spatial signals for large scale imaging data. Typically, the spatial signals are sparse but clustered. This paper provides empirical evidence that for a range of commonly used control levels, the conventional FDR procedure can lack the ability to detect statistical significance, even if the p-values under the true null hypotheses are independent and uniformly distributed; more generally, ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the FDR procedure. This paper first introduces a scalar quantity to characterize the extent to which the lack of identification phenomenon(LIP) of the FDR procedure occurs. Second, we propose a new multiple comparison procedure, called FDR L, to accommodate the spatial information of neighboring p-values, via a local aggregation of p