Note on a product formula for unitary groups
Vincent Cachia
Abstract
For any nonnegative self-adjoint operators A and B in a separable Hilbert space, we show that the Trotter-type formula [(ei2tA/n+ei2tB/n)/2]n converges strongly in the closure of the intersection of the domains of A1/2 and B1/2, along some subsequence and for almost every real number t. This result extends to the degenerate case and to Kato-functions following the method of Kato.
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