### $\u2102$-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation.

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A positive operator A and a closed subspace of a Hilbert space ℋ are called compatible if there exists a projector Q onto such that AQ = Q*A. Compatibility is shown to depend on the existence of certain decompositions of ℋ and the ranges of A and ${A}^{1/2}$. It also depends on a certain angle between A() and the orthogonal of .