Note on a product formula for unitary groups

Details Note on a product formula for unitary groups Note on a product formula for unitary groups

2004-04-22

arxiv.org/abs/math/0404409v1

Bulletin London Math. Soc. 37 (2005), 621-626

Mathematics

Functional Analysis

5 pages, submitted to the London Math. Soc

Scientific paper

10.1112/S0024609305004479

For any nonnegative self-adjoint operators A and B in a separable Hilbert space, we show that the Trotter-type formula $[(e^{i2tA/n}+e^{i2tB/n})/2]^n$ converges strongly in the closure of the intersection of the domains of A^{1/2} and B^{1/2}, 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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