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...

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

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...

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

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...

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...

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

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

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

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

other topologies rather than the standard one: If X {\displaystyle X} is the real numbers R {\displaystyle \mathbb {R} } with the lower limit topology, then...

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

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

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...

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

can put other topologies rather than the standard one. If X = R {\displaystyle X=\mathbb {R} } is endowed with the lower limit topology, then cl X ⁡ (...

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

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

semigroup (R+, +) on some Banach space X that is continuous in the strong operator topology. A strongly continuous semigroup on a Banach space X {\displaystyle...

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...

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

any induced topology (relative to the subset A) the closed sets induce a new closure operator that is just the original closure operator restricted to...

possible topologies on a fixed set X are partially ordered: a topology τ 1 {\displaystyle \tau _{1}} is said to be coarser than another topology τ 2 {\displaystyle...

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,...

preserve the weak operator topology. As it turns out (and follows easily from the definitions), for algebras L∞(X, μ), the following topologies agree on norm...

generates the topology T. Bases are useful because many properties of topologies can be reduced to statements about a base that generates that topology—and because...

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

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