functional analysis there are several standard topologies which are given to the algebra B(X) of bounded linear operators on a Banach space X. Let ( T n ) n ∈ N...
10 KB (1,487 words) - 20:43, 17 June 2024
mathematics, the strong operator topology, often abbreviated SOT, is the locally convex topology on the set of bounded operators on a Hilbert space H induced...
3 KB (489 words) - 08:51, 4 December 2022
mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance...
22 KB (3,110 words) - 12:28, 31 May 2024
common topologies on B ( H ) {\displaystyle B(H)} , the bounded operators on a Hilbert space H {\displaystyle H} . The strong operator topology, or SOT...
9 KB (1,633 words) - 02:57, 18 October 2023
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics....
15 KB (2,023 words) - 17:43, 23 May 2024
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...
3 KB (380 words) - 04:42, 31 January 2024
Von Neumann bicommutant theorem (category Operator theory)
topologies on the space of bounded operators, and one can ask what are the *-algebras closed in these topologies. If M is closed in the norm topology...
7 KB (928 words) - 14:43, 22 July 2024
variety of topologies. Studying space of linear maps and these topologies can give insight into the spaces themselves. The article operator topologies discusses...
37 KB (6,521 words) - 12:27, 14 May 2024
a strong topology is a topology which is stronger than some other "default" topology. This term is used to describe different topologies depending on...
918 bytes (155 words) - 20:08, 28 August 2016
possible topologies. See topologies on the set of operators on a Hilbert space for some intricate relationships. All possible polar topologies on a dual...
8 KB (981 words) - 02:22, 28 June 2024