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Ultraweak Topology
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Geliefert zwischen Do., 27.11.2025 und Fr., 28.11.2025
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High Quality Content by WIKIPEDIA articles! The ultraweak topology is similar to the weak operator topology. For example, on any norm-bounded set the weak operator and ultraweak topologies are the same, and in particular the unit ball is compact in both topologies. The ultraweak topology is stronger than the weak operator topology. One problem with the weak operator topology is that the dual of B(H) with the weak operator topology is "too small". The ultraweak topology fixes this problem: the dual is the full predual B (H) of all trace class operators. In general the ultraweak topology is more useful than the weak operator topology, but it is more complicated to define, and the weak operator topology is often more apparently convenient. The ultraweak topology can be obtained from the weak operator topology as follows. If H1 is a separable infinite dimensional Hilbert space then B(H) can be embedded in B(H H1) by tensoring with the identity map on H1. Then the restriction of the weak operator topology on B(H H1) is the ultraweak topology of B(H).
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131169526
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131169526
- Format Fachbuch
- Titel Ultraweak Topology
- Herausgeber Betascript Publishing
- Anzahl Seiten 116
- Genre Informatik
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