OAI.KadisonSimilarity.universalHyperreflexivity

The theorem states that the explicit absolute constant universalConstant makes the universal hyperreflexivity property hold, for Hilbert spaces in the fixed universe u. Here universalConstant = 3·factorConstant + 2, where factorConstant = max(3·cornerConstant + 2, 1 + 2·rowConstant, 2), cornerConstant = 6π²(1 + 4·cyclicConstant), cyclicConstant = (1 + 4·rowConstant)², and rowConstant = 4√2. The property UniversalHyperreflexivity(C) says that for every complex Hilbert space K in that universe, every von Neumann algebra M of operators on K, and every bounded operator T on K, the operator-norm distance from T to the set M is at most 2·C·offDiagonalSeminorm(M,T). The off-diagonal seminorm is the supremum, over all projections e in the commutant of M (self-adjoint idempotent bounded operators commuting with M), of the norm ‖(1 − e) T e‖. So the theorem gives, with C = universalConstant, dist(T, M) ≤ 2·universalConstant·sup_e ‖(1 − e) T e‖ for all such K, M and T.