Counterexample to the Trotter product formula for projections
Mate Matolcsi, Roman Shvidkoy
Abstract
We constructed a unitary semigroup (etA)t ≥ 0 on a Hilbert space and an orthogonal projection P such that the limit n ∞ [ etnAP ]n does not exist strongly. A similar example with a positive contractive semigroup and positive contractive projection on Lp is also constructed.
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