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...

topology.) The σ-weak topology or ultraweak topology or weak-* operator topology or weak-* topology or weak topology or σ(B(H), B(H)*) topology is defined by...

operator topology if and only if ‖ T i x − T x ‖ → 0 {\displaystyle \|T_{i}x-Tx\|\to 0} for each x in H. The SOT is stronger than the weak operator topology...

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...

contains its weak operator closure. This follows directly from the weak operator topology being coarser than the strong operator topology: for every point...

*-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type...

norm bounded sets: The weak operator topology on L∞(X, μ); The ultraweak operator topology on L∞(X, μ); The topology of weak* convergence on L∞(X, μ)...

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

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....

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

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

Terytorialnej, a Polish reserve force Wot, Nepal Wang-an Airport, Taiwan Weak operator topology, in functional analysis Web of Things, objects connected to the...

linear operators on a complex Hilbert space with two additional properties: A is a topologically closed set in the norm topology of operators. A is closed...

the Jordan algebra of self-adjoint operators on a complex Hilbert space that is closed in the weak operator topology. A JBW algebra is a JB algebra that...

structure. Vertex operator algebra Von Neumann algebra: a *-algebra of operators on a Hilbert space equipped with the weak operator topology. Algebraic structures...

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 (or smaller, weaker)...

In topology, an Alexandrov topology is a topology in which the intersection of every family of open sets is open. It is an axiom of topology that the...

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

In other words, the double commutant is the closure of A in the weak operator topology. See also the Kaplansky density theorem in the von Neumann algebra...

universal representation of a C*-algebra A, the closure of Φ(A) in the weak operator topology is called the enveloping von Neumann algebra of A. It can be identified...

normed vector space is compact in the weak* topology. A common proof identifies the unit ball with the weak-* topology as a closed subset of a product of...

calculus has a larger range, that is the closure of C(T) in the weak operator topology, a (still abelian) von Neumann algebra. We can also define the functional...

f\!\left(y\right)} .) To avoid ambiguity, the terms weakly monotone, weakly increasing and weakly decreasing are often used to refer to non-strict monotonicity...

there is a topology weaker than the weak topology of X ′ , {\displaystyle X^{\prime },} called weak* topology. It is the coarsest topology on X ′ {\displaystyle...

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 ≤ ∞ then...

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

realised as Jordan algebras of self-adjoint operators on a Hilbert space closed in the weak operator topology. Of these the spin factors can be constructed...

C*-subalgebra of bounded operators on HU. The enveloping von Neumann algebra of A is the closure of πU(A) in the weak operator topology. It is sometimes denoted...

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