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searching for Continuous linear operator 19 found (53 total)

alternate case: continuous linear operator

Hypercyclic operator (529 words) [view diff] exact match in snippet view article find links to article

a hypercyclic operator on a topological vector space X is a continuous linear operator T: X → X such that there is a vector x ∈ X for which the sequence

Integral linear operator (2,168 words) [view diff] exact match in snippet view article find links to article

vector spaces (TVSs) X and Y. An integral linear operator is a continuous linear operator that arises in a canonical way from an integral bilinear form

Transpose of a linear map (2,716 words) [view diff] exact match in snippet view article find links to article

Suppose now that u : X → Y {\displaystyle u:X\to Y} is a weakly continuous linear operator between topological vector spaces X {\displaystyle X} and Y {\displaystyle

Fredholm solvability (404 words) [view diff] exact match in snippet view article find links to article

spaces and let T : E → F {\displaystyle T:E\rightarrow F} be a continuous linear operator. Let E ∗ {\displaystyle E^{*}} , respectively F ∗ {\displaystyle

Nuclear operator (4,791 words) [view diff] exact match in snippet view article find links to article

Banach spaces and that N : X → Y {\displaystyle N:X\to Y} is a continuous linear operator. The following are equivalent: N : X → Y {\displaystyle N:X\to

Hermitian adjoint (3,270 words) [view diff] exact match in snippet view article find links to article

⟩ {\displaystyle \langle \cdot ,\cdot \rangle } . Consider a continuous linear operator A : H → H (for linear operators, continuity is equivalent to being

Operator theory (1,638 words) [view diff] exact match in snippet view article find links to article

operator on a complex Hilbert space H {\displaystyle H} is a continuous linear operator N : H → H {\displaystyle N\colon H\rightarrow H} that commutes

Hilbert–Schmidt operator (1,391 words) [view diff] exact match in snippet view article find links to article

{\displaystyle (x\otimes y)(z)=\langle z,y\rangle x} , which is a continuous linear operator of rank 1 and thus a Hilbert–Schmidt operator; moreover, for any

Bochner integral (2,196 words) [view diff] exact match in snippet view article find links to article

functions. If T : B → B ′ {\displaystyle T\colon B\to B'} is a continuous linear operator between Banach spaces B {\displaystyle B} and B ′ {\displaystyle

Glossary of functional analysis (3,200 words) [view diff] exact match in snippet view article find links to article

unit group of A. open The open mapping theorem says a surjective continuous linear operator between Banach spaces is an open mapping. orthonormal 1. A subset

Spectrum (functional analysis) (5,808 words) [view diff] exact match in snippet view article

definitions of the resolvent and spectrum can be extended to any continuous linear operator T {\displaystyle T} acting on a Banach space X {\displaystyle

Projection (linear algebra) (5,806 words) [view diff] exact match in snippet view article

Furthermore, the kernel of a continuous projection (in fact, a continuous linear operator in general) is closed. Thus a continuous projection P {\displaystyle

Dual space (6,865 words) [view diff] exact match in snippet view article find links to article

the algebraic double dual, there is always a naturally defined continuous linear operator Ψ : V → V′′ from a normed space V into its continuous double dual

Minlos–Sazonov theorem (1,027 words) [view diff] exact match in snippet view article find links to article

) ≤ C q ( x ) , {\displaystyle p(x)\leq Cq(x),} then define a continuous linear operator T q , p : X ¯ q → X ¯ p {\displaystyle T_{q,p}:{\overline {X}}_{q}\to

Compact operator on Hilbert space (4,868 words) [view diff] exact match in snippet view article find links to article

wikidata descriptions as a fallback Compact operator – Type of continuous linear operator Decomposition of spectrum (functional analysis) – Construction

Open and closed maps (5,297 words) [view diff] exact match in snippet view article find links to article

analysis, the open mapping theorem states that every surjective continuous linear operator between Banach spaces is an open map. This theorem has been generalized

Moore–Penrose inverse (7,644 words) [view diff] exact match in snippet view article find links to article

conditions as in our definition above. It turns out that not every continuous linear operator has a continuous linear pseudoinverse in this sense. Those that

Hilbert projection theorem (3,544 words) [view diff] exact match in snippet view article find links to article

{\displaystyle A:\mathbb {R} ^{2}\to \mathbb {R} ^{2}} is an invertible continuous linear operator that satisfies A ( L s ) = L s / r {\displaystyle A\left(L_{s}\right)=L_{s/r}}

Representation theory of finite groups (21,294 words) [view diff] no match in snippet view article find links to article

{\displaystyle G} are called equivalent, if there exists a bijective, continuous, linear operator T {\displaystyle T} between the representation spaces whose inverse