Closure operator
Closure operator In mathematics, given a partially ordered set (P, ≤), a closure operator on P is a function C : P ... comes from the fact that forming the closure of subsets of a topological space ...
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Talk:Closure operator
Talk:Closure operator Useful - my thanks to Axel for pulling ...
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Closure (topology)
Closure (topology) In mathematics, the closure of a set S consists of all ... S". A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to ...
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Closed operator
Closed operator In mathematics, specifically in functional analysis, closed ... math> denote a Banach space. A linear operator $A\backslash colon\backslash mathcal\{D\}(A)\backslash subset\; ...\; B\backslash oplus\; B.$ Given a linear operator $A$, not necessarily closed, if the closure of its graph in $B\backslash oplus\; ...\; happens\; to\; be\; the\; graph\; of\; some$operator, that operator is called the closure ...
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Compact operator
Compact operator In functional analysis, a compact operator (or completely continuous operator) is a linear operator L from a Banach space X to ... relatively compact subset of Y. Such an operator is necessarily a bounded operator, and ...
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Operator algebra
Operator algebra In functional analysis, an operator algebra is an algebra of continuous linear ... required to be closed in a specified operator topology. In particular, it is a set ... of operators with both algebraic and topological closure properties. Though operator algebras are studied in this generality ...
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Closure (mathematics)
Closure (mathematics) In mathematics, the closure C(X) of an object X is ... closed if it is equal to its closure. Typical structural properties of all closure operations are: The closure is increasing or extensive: the closure ...
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Kuratowski closure axioms
Kuratowski closure axioms In topology and related branches of mathematics, the Kuratowski closure axioms are a set of axioms which ... using only the dual notion of interior operator. Definition A topological space $(X,cl\; ...\; to\; \backslash mathcal\{P\}(X)$ called the closure operator where $\backslash mathcal\{P\}(X)$ ...
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Strong operator topology
Strong operator topology In functional analysis, the strong operator topology, often abbreviated SOT, is the weakest ... such that the evaluation map sending an operator T to the real number $\backslash |Tx\; ...\; The\; SOT\; is\; stronger\; than\; the\; weak$operator topology and weaker than the norm topology ... of the nicer properties that the weak operator topology has, but being stronger, things ...
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Weak operator topology
Weak operator topology In functional analysis, the weak operator topology, often abbreviated WOT, is the weakest ... space such that the functional sending an operator T to the complex number $\backslash langle\; ...\; The\; WOT\; is\; weaker\; than\; the\; strong$operator topology and weaker than the norm topology ... space which are continuous in the strong operator topology are precisely those which are ...
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