Operator topologies information

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...

mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance...

common topologies on B ( H ) {\displaystyle B(H)} , the bounded operators on a Hilbert space H {\displaystyle H} . The strong operator topology, or SOT...

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...

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...

The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics....

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...

variety of topologies. Studying space of linear maps and these topologies can give insight into the spaces themselves. The article operator topologies discusses...

mechanics – Formulation of quantum mechanics Topologies on the set of operators on a Hilbert space Vertex operator algebra – Algebra used in 2D conformal field...

a strong topology is a topology which is stronger than some other "default" topology. This term is used to describe different topologies depending on...

possible topologies. See topologies on the set of operators on a Hilbert space for some intricate relationships. All possible polar topologies on a dual...

many other common topologies including the strong, ultrastrong or ultraweak operator topologies. The *-algebras of bounded operators that are closed in...

open sets is open; in Alexandrov topologies the finite restriction is dropped. A set together with an Alexandrov topology is known as an Alexandrov-discrete...

set the strong operator and ultrastrong topologies are the same. The ultrastrong topology is stronger than the strong operator topology. One problem with...

linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function...

space H, the compact operators are the closure of the finite rank operators in the uniform operator topology. In general, operators on infinite-dimensional...

density Topologies on the set of operators on a Hilbert space norm topology ultrastrong topology strong operator topology weak operator topology weak-star...

redirect targets Operator algebra – Branch of functional analysis Operator theory – Mathematical field of study Topologies on the set of operators on a Hilbert...

(as opposed to weak convergence). The convergence of operators in the strong operator topology. This disambiguation page lists articles associated with...

the closure of finite-rank operators (representable by finite-dimensional matrices) in the topology induced by the operator norm. As such, results from...

\}\cup \Gamma } is a topology on X . {\displaystyle X.} Many sets of linear operators in functional analysis are endowed with topologies that are defined...

unitary operators on H. Then the operator 1 T ∫ 0 T U t d t {\displaystyle {\frac {1}{T}}\int _{0}^{T}U_{t}\,dt} converges in the strong operator topology as...

with a topology defined by convex open sets Operator theory – Mathematical field of study Operator topologies – Topologies on the set of operators on a...

functionals continuous for the weak or strong topologies. As a consequence the weak and strong topologies coincide on a JBW algebra. In a JBW algebra,...

which prevents confusion with the "closure operators" studied in topology. E. H. Moore studied closure operators in his 1910 Introduction to a form of general...

structure. Vertex operator algebra Von Neumann algebra: a *-algebra of operators on a Hilbert space equipped with the weak operator topology. Algebraic structures...