|
|||||
|
|
Diagonalization and representation results for nonpositive sesquilinear form measures |
|
| Authors: | Tuomas Hytö nen,Kari Ylinen |
| Affiliation: | a Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin katu 2b, FI-00014 Helsinki, Finland b Department of Physics, University of Turku, FI-20014 Turku, Finland c Department of Mathematics, University of Turku, FI-20014 Turku, Finland |
| Abstract: | We study decompositions of operator measures and more general sesquilinear form measures E into linear combinations of positive parts, and their diagonal vector expansions. The underlying philosophy is to represent E as a trace class valued measure of bounded variation on a new Hilbert space related to E. The choice of the auxiliary Hilbert space fixes a unique decomposition with certain properties, but this choice itself is not canonical. We present relations to Naimark type dilations and direct integrals. |
| Keywords: | Sesquilinear form Operator measure Bounded variation Diagonalization Naimark dilation Direct integral |
| 本文献已被 ScienceDirect 等数据库收录！ | |