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...

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

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

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

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

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

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

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

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...

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...

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

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...

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...

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

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...

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

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...

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

f^{-1}({\bar {s}})} . Grothendieck topologies on a small category C are essentially the same as Lawvere–Tierney topologies on the topos of presheaves of sets...

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...

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

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...

properties. They are non-selfadjoint algebras, are closed in the weak operator topology and are reflexive. Nest algebras are among the simplest examples of...