Note on a product formula for unitary groups

Abstract

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.

5 pages, submitted to the London Math. Soc

References in corpus (1)

• Product formula related to quantum Zeno dynamics

Cited by in corpus (1)

• Trotter-Kato product formula for unitary groups