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Kato’s inequality and the comparison of semigroups. (English) Zbl 0413.47037


MSC:

47B60 Linear operators on ordered spaces
47D03 Groups and semigroups of linear operators
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[1] Avron, J.; Herbst, I.; Simon, B., Schrödinger operators with magnetic fields. I. General theory, Duke Math. J., 45, 847-883 (1978) · Zbl 0399.35029
[2] Beurling, A.; Deny, J., Espaces de Dirichlet, Acta Math., 99, 203-224 (1958) · Zbl 0089.08106
[3] Combes, J.; Schrader, R.; Seiler, R., Classical bounds and limits for energy distributions of Hamiltonian operators in electromagnetic fields, Ann. Phys. (New York), 111, 1-18 (1978), preprint
[4] Davies, E. B., Properties of Green’s function of some Schrödinger operators, J. London Math. Soc., 7, 473-491 (1973) · Zbl 0271.47003
[5] Ikebe, T.; Kato, T., Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. Rational Mech. Anal., 9, 77-92 (1962) · Zbl 0103.31801
[6] Kato, T., Schrödinger operators with singular potential, Israel J. Math., 13, 135-148 (1972)
[7] Reed, M.; Simon, B., Methods of Modern Mathematical Physics. IV. Analysis of Operators (1978), Academic Press: Academic Press New York · Zbl 0401.47001
[8] Schechter, M., Spectra of Partial Differential Operators (1971), North-Holland: North-Holland Amsterdam · Zbl 0225.35001
[9] Simon, B., Schrödinger operators with singular magnetic vector potential, Math. Z., 131, 361-370 (1973) · Zbl 0277.47006
[10] Simon, B., Universal diamagnetism of spinless Bose systems, Phys. Rev. Lett., 36, 1083-1084 (1976)
[11] Simon, B., Abstract Kato’s inequality for generators of positivity preserving semigroups, Indiana Univ. Math. J., 26, 1067-1073 (1977) · Zbl 0389.47021
[12] Simon, B., Functional Integration and Quantum Physics (1979), Academic Press: Academic Press New York · Zbl 0434.28013
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