Counterexample to the Trotter product formula for projections

2001/09/07 by Máté Matolcsi, Mate Matolcsi, Matolcsi, Mate +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #47d03 #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.FA #msc:47d03

paper · pdf · doi:10.48550/arxiv.math/0109049

arxiv created 2001/09/07 · openalex publication_date 2001/09/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We constructed a unitary semigroup (e^tA)_{t ≥ 0} on a Hilbert space and an orthogonal projection P such that the limit lim_{n → ∞} [ e^(t)/(n)AP ]ⁿ does not exist strongly. A similar example with a positive contractive semigroup and positive contractive projection on L_p is also constructed.

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