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, 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....

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

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...

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

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...

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

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...

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

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

referred to such topologies as Alexandrov topologies. F. G. Arenas independently proposed this name for the general version of these topologies. McCord also...

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...

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

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

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

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...

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...

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...

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

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 ⁡ (...

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...

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

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

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...

closure of S. Closure operator See Kuratowski closure axioms. Coarser topology If X is a set, and if T1 and T2 are topologies on X, then T1 is coarser...