Absolute continuity for unbounded positive self-adjoint operators. (English) Zbl 1478.47015
Summary: The notion of absolute continuity for positive operators was studied by T. Ando [Acta Sci. Math. 38, 253–260 (1976; Zbl 0337.47011)], where parallel sums for such operators played an important role. On the other hand, a theory for parallel sums for densely defined positive self-adjoint operators (or more generally positive forms) was developed in our previous work [Kyushu J. Math. 71, No. 2, 387–405 (2017; Zbl 1470.47005)]. Based on this theory, we investigate the notion of absolute continuity in such unbounded cases.
MSC:
| 47B25 | Linear symmetric and selfadjoint operators (unbounded) |
| 47A07 | Forms (bilinear, sesquilinear, multilinear) |
| 47A64 | Operator means involving linear operators, shorted linear operators, etc. |
Keywords:
absolute continuity; absolutely continuous part; maximal closable part; parallel sum; positive form; positive self-adjoint operator; quadratic formReferences:
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