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An estimate of the Kac transfer operator. (English) Zbl 0919.47031
The authors compare the exponential group of a Schrödinger operator with the corresponding Kac transfer operator. The result of B. Helffer [Oper. Theory, Adv. Appl. 78, 161-174 (1995; Zbl 0835.47050)] is derived here in a more general setting and by different methods that rely on holomorphic semigroups and estimates of commutators.

MSC:
47D06 One-parameter semigroups and linear evolution equations
47B65 Positive linear operators and order-bounded operators
47B38 Linear operators on function spaces (general)
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[1] Dia, B.O.; Schatzman, M., Commutateurs de certains semi-groupes holomorphes et applications aux directions alternées, Modél. math. anal. num. (MZAN), 30, 343-383, (1996) · Zbl 0853.47024
[2] Helffer, B., Around the transfer operator and the trotter – kato formula, Oper. theory: adv. appl., 78, 161-174, (1995) · Zbl 0835.47050
[3] Kato, T., Perturbation theory for linear operators, (1966), Springer-Verlag Berlin · Zbl 0148.12601
[4] Riesz, F., Leçons d’analyse fonctionnelle, (1952), Akadémiai Kiadó Budapest
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