Orthogonal Apartments in Hilbert Grassmannians
نویسنده
چکیده
Let H be an infinite-dimensional complex Hilbert space and let L(H) be the logic formed by all closed subspaces of H. For every natural k we denote by Gk(H) the Grassmannian consisting of k-dimensional subspaces. An orthogonal apartment of Gk(H) is the set consisting of all k-dimensional subspaces spanned by subsets of a certain orthogonal base of H. Orthogonal apartments can be characterized as maximal sets of mutually compatible elements of Gk(H). We show that every bijective transformation f of Gk(H) such that f and f send orthogonal apartments to orthogonal apartments (in other words, f preserves the compatibility relation in both directions) can be uniquely extended to an automorphism of L(H).
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