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Corrigendum to the paper “ergodicity in classical and quantum statistical mechanics”
Vol. 9 (1976)
REPORTS
ON MATHEMATICAL
No.
PHYSICS
CORRIGENDUM TO THE PAPER “ERGODICITY IN CLASSICAL QUANTUM STATISTICAL MECHANICS”
3
AND
Reports Math. Phys. 9 (1976), 1
W. Guz Institute
of Physics,
Gdadsk
University,
Gdalisk,
Poland
(Received October 4, 1976)
The positive cone X+ of the partially ordered real Banach space X (see p. 1 of the paper) would be assumed to be a norm-closed subset of X. Theorem 1.4 on p. 4 was unprecisely stated. It should be formulated as follows: THEOREM 1.4. Any dynamical semigroup T,, t 2 0, satisfying condition (I) and being strongly Abelian ergodic in 03 has an .invariant non-zero state if for some x # 0 one has
(A)- lim 7+,x # 0. 1-m Another theorem in our paper, Theorem 2.3 on p. 6, although stated correctly together with the proof, is not original. It can be found, for instance, in the Riesz and Nagy’s Functional anaIysis (2nd ed., Ungar, New ,York, 1955), pp. 407, 409. The author is indebted to Dr J.C. Wolfe (University of Vancouver, ,Canada) for difecting attention to this reference and pointing out the unprecise formulation of Theorem 1.4.
14231
REPORTS
ON MATHEMATICAL
No.
PHYSICS
CORRIGENDUM TO THE PAPER “ERGODICITY IN CLASSICAL QUANTUM STATISTICAL MECHANICS”
3
AND
Reports Math. Phys. 9 (1976), 1
W. Guz Institute
of Physics,
Gdadsk
University,
Gdalisk,
Poland
(Received October 4, 1976)
The positive cone X+ of the partially ordered real Banach space X (see p. 1 of the paper) would be assumed to be a norm-closed subset of X. Theorem 1.4 on p. 4 was unprecisely stated. It should be formulated as follows: THEOREM 1.4. Any dynamical semigroup T,, t 2 0, satisfying condition (I) and being strongly Abelian ergodic in 03 has an .invariant non-zero state if for some x # 0 one has
(A)- lim 7+,x # 0. 1-m Another theorem in our paper, Theorem 2.3 on p. 6, although stated correctly together with the proof, is not original. It can be found, for instance, in the Riesz and Nagy’s Functional anaIysis (2nd ed., Ungar, New ,York, 1955), pp. 407, 409. The author is indebted to Dr J.C. Wolfe (University of Vancouver, ,Canada) for difecting attention to this reference and pointing out the unprecise formulation of Theorem 1.4.
14231