Abstract
LetH andK be lower-bounded self-adjoint operators whose form sum is denoted byH \(\hat + \) K. We show the norm inequality\(||e^{ - (H\hat + K)} ||\) ⩽ ∥(e−rH/2 e−rK e−rH/2)1/r ∥ forr > 0 and any symmetric norm ∥•∥. WhenH +K is essentially self-adjoint and e−K is of trace class, we prove that (e−rH/2e−rKe−rH/2)1/r converges asr ↓ 0 to e−(H+K) in the trace norm.
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