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, the strong operator topology, often abbreviated SOT, is the locally convex topology on the set of bounded operators on a Hilbert space H induced...

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...

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...

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...

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...

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

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

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

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...

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

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...

Hilbert space H {\displaystyle {\mathcal {H}}} endowed with the strong operator topology is metrizable (see Proposition II.1 in ). Examples of non-metrizable...

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...

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

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...

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 ⁡ (...

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...

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...

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

X {\displaystyle X} has infinitely many distinct vector topologies: Some of these topologies are now described: Every linear functional f {\displaystyle...

P.J. Morandi. The McKinsey–Tarski topology of an interior algebra is the intersection of the former two topologies. Grzegorczyk proved the first-order...

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

space definition of weak convergence. Dual topology Operator topologies – topologies on the set of operators on a Hilbert space "redirect". dept.math.lsa...

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...