branch of mathematics, a closed linear operator or often a closed operator is a linear operator whose graph is closed (see closed graph property). It is...

space; this linear subspace is not necessarily closed; often (but not always) it is assumed to be dense; in the special case of a bounded operator, still,...

continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. An operator between two...

particularly in functional analysis, the closed graph theorem is a result connecting the continuity of a linear operator to a topological property of their...

In functional analysis and operator theory, a bounded linear operator is a linear transformation L : X → Y {\displaystyle L:X\to Y} between topological...

honour of Erik Ivar Fredholm. By definition, a Fredholm operator is a bounded linear operator T : X → Y between two Banach spaces with finite-dimensional...

a linear endomorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different...

characteristics, such as bounded linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily...

else}}\end{cases}}} . Also, closed linear operators in functional analysis (linear operators with closed graphs) are typically not continuous. Closed graph theorem...

In functional analysis, a branch of mathematics, a compact operator is a linear operator T : X → Y {\displaystyle T:X\to Y} , where X , Y {\displaystyle...

the essential spectrum of a bounded operator (or, more generally, of a densely defined closed linear operator) is a certain subset of its spectrum,...

functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues...

the object. A projection on a vector space V {\displaystyle V} is a linear operator P : V → V {\displaystyle P\colon V\to V} such that P 2 = P {\displaystyle...

mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its operator norm. Formally, it...

the generators of strongly continuous one-parameter semigroups of linear operators on Banach spaces. It is sometimes stated for the special case of contraction...

In mathematical analysis, an integral linear operator is a linear operator T given by integration; i.e., ( T f ) ( x ) = ∫ f ( y ) K ( x , y ) d y {\displaystyle...

specifically in operator theory, each linear operator A {\displaystyle A} on an inner product space defines a Hermitian adjoint (or adjoint) operator A ∗ {\displaystyle...

map. Closed graph – Graph of a map closed in the product spacePages displaying short descriptions of redirect targets Closed linear operator – Linear operator...

discontinuous linear map everywhere on a complete space. Many naturally occurring linear discontinuous operators are closed, a class of operators which share...

be Banach spaces, T : D ( T ) → Y {\displaystyle T:D(T)\to Y} a closed linear operator whose domain D ( T ) {\displaystyle D(T)} is dense in X , {\displaystyle...

operations is the smallest superset that is closed under these operations. It is often called the span (for example linear span) or the generated set. Let S be...

× Y. In particular, the term "closed linear operator" will almost certainly refer to a linear map whose graph is closed. Otherwise, especially in literature...

[clarification needed] A closed operator that is used in practice is often densely defined. A densely defined linear operator T {\displaystyle T} from...

finite-dimensional, then a linear operator L: V → W is continuous if and only if the kernel of L is a closed subspace of V. Consider a linear map represented as...

is a fundamental result that states that if a bounded or continuous linear operator between Banach spaces is surjective then it is an open map. A special...

mathematics, specifically in spectral theory, a discrete spectrum of a closed linear operator is defined as the set of isolated points of its spectrum such that...

functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication...

Closure operators are determined by their closed sets, i.e., by the sets of the form cl(X), since the closure cl(X) of a set X is the smallest closed set...

Hilbert–Schmidt operator T : H → H is a compact operator. A bounded linear operator T : H → H is Hilbert–Schmidt if and only if the same is true of the operator | T...

complete metrizable TVS. Every closed linear operator from X {\displaystyle X} into a complete metrizable TVS is continuous. A linear map F : X → Y {\displaystyle...