Geodesic
Positive Perturbations and Unitary Equivalence
Canadian journal of mathematics, Tome 29 (1977) no. 1, pp. 161-164

Voir la notice de l'article provenant de la source Cambridge University Press

Let T be a (not necessarily bounded) self-adjoint operator on a Hilbert space H with the spectral resolution The set of elements x in H for which ||Etx||2 is absolutely continuous is a subspace, H a, of H which reduces T. (See H almos [1, p. 104]; Kato [2, p. 516].) If H a ≠ 0, the restriction of T to DT ⋂ H a is called the absolutely continuous part of T; in case H = H a, T is said to be absolutely continuous. 
Putnam, C. R. Positive Perturbations and Unitary Equivalence. Canadian journal of mathematics, Tome 29 (1977) no. 1, pp. 161-164. doi: 10.4153/CJM-1977-015-0
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