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

the final topology on the disjoint union the topology arising from a norm the strong operator topology the strong topology (polar topology), which subsumes...

x\in X} , then we say T n → T {\displaystyle T_{n}\to T} in the strong operator topology. Finally, suppose that for all x ∈ X {\displaystyle x\in X} we...

functional analysis, the weak operator topology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space H {\displaystyle...

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

adjoints. Then the closures of M in the weak operator topology and the strong operator topology are equal, and are in turn equal to the bicommutant M′′...

strongly continuous semigroup is a representation of the semigroup (R+, +) on some Banach space X that is continuous in the strong operator topology....

The convergence of operators in the strong operator topology. This disambiguation page lists articles associated with the title Strong convergence. If an...

equipped with the strong (dual) topology or the topology of uniform convergence on bounded subsets of X , {\displaystyle X,} where this topology is denoted by...

ultrastrong topology, or σ-strong topology, or strongest topology on the set B(H) of bounded operators on a Hilbert space is the topology defined by the...

converge to the projector ET in the strong operator topology of Lp if 1 ≤ p ≤ ∞, and in the weak operator topology if p = ∞. More is true if 1 < p ≤ ∞...

explicitly defined the weak topology on Hilbert spaces and strong operator topology on operators on Hilbert spaces. Finally, in 1935 von Neumann introduced...

ultraweak topology, also called the weak-* topology, or weak-* operator topology or σ-weak topology, is a topology on B(H), the space of bounded operators on...

Strong operator topology Topologies on spaces of linear maps Ultrastrong topology Ultraweak topology/weak-* operator topology Weak operator topology Inductive...

Then the topology τ1 is said to be a coarser (weaker or smaller) topology than τ2, and τ2 is said to be a finer (stronger or larger) topology than τ1....

the identity operator would be compact, a contradiction. If sequences of bounded operators Bn → B, Cn → C in the strong operator topology and T is compact...

of Toxicology, U.S. Sound on tape, in television broadcasting Strong operator topology, in mathematics Sot (village), Vojvodina, Serbia Sodankylä Airfield...

In topology, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of...

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...

mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H. It states that...

the strong operator topology to H. Moreover, if Vf(z) = f(H(z)), then VHV−1 − H is an operator with smooth kernel, so a Hilbert–Schmidt operator. In fact...

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...

the strong operator topology to H. Moreover, if Vf(z) = f(H(z)), then VHV−1 – H is an operator with smooth kernel, so a Hilbert–Schmidt operator. The...

in the strong operator topology of L(V), it is independent of the chosen basis of W. The partial trace TrW(T) is defined to be this operator. The partial...

is a separable topological group, Φ is continuous in the strong (or weak) operator topology if and only if U is. In this case functions supported on a...

operator topology is metrizable (see Proposition II.1 in ). Non-normal spaces cannot be metrizable; important examples include the Zariski topology on...

a homomorphism into the bounded invertible operators which is continuous for the strong operator topology, and such that sup g ∈ G ‖ T g ‖ B ( H ) {\displaystyle...

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

groups. The unitary group of a separable Hilbert space (with the strong operator topology) is a Polish group. The group of homeomorphisms of a compact metric...