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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...

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...

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

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...

*-representations of A on Hn with the point-weak topology. In terms of convergence of nets, this topology is defined by πi → π; if and only if ⟨ π i (...

In topology and related branches of mathematics, the Kuratowski closure axioms are a set of axioms that can be used to define a topological structure on...

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)...

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...

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...

*-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...

Order topology of a total order (open interval topology) Alexandrov topology Upper topology Scott topology Scott continuity Lawson topology Finer topology...

{\displaystyle J,} but the topology on X {\displaystyle X} (the weak topology of Y {\displaystyle Y} ) is not the strong topology β ( X , X ′ ) , {\displaystyle...

convex topologies were implicitly used by some mathematicians, up to 1934 only John von Neumann would seem to have explicitly defined the weak topology on...

to order theory and the closure operator of sets can be used to define a topology. Beyond these relations, topology can be looked at solely in terms...

properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics, glossary of category theory...

Galois connection. Alexandrov topology. For a preordered set P, any upper set O is Alexandrov-open. Inversely, a topology is Alexandrov if any intersection...

union. The topologies on a set, when ordered by inclusion. The infimum is given by the intersection of topologies, and the supremum by the topology generated...

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...

Homotopical algebra; Topology using categories, including algebraic topology, categorical topology, quantum topology, low-dimensional topology; Categorical logic...