Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Compact_operator> ?p ?o }
- Compact_operator abstract "In functional analysis, a branch of mathematics, a compact operator is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset of Y. Such an operator is necessarily a bounded operator, and so continuous.Any bounded operator L that has finite rank is a compact operator; indeed, the class of compact operators is a natural generalisation of the class of finite-rank operators in an infinite-dimensional setting. When Y is a Hilbert space, it is true that any compact operator is a limit of finite-rank operators, so that the class of compact operators can be defined alternatively as the closure in the operator norm of the finite-rank operators. Whether this was true in general for Banach spaces (the approximation property) was an unsolved question for many years; in the end Per Enflo gave a counter-example.The origin of the theory of compact operators is in the theory of integral equations, where integral operators supply concrete examples of such operators. A typical Fredholm integral equation gives rise to a compact operator K on function spaces; the compactness property is shown by equicontinuity. The method of approximation by finite-rank operators is basic in the numerical solution of such equations. The abstract idea of Fredholm operator is derived from this connection.".
- Compact_operator wikiPageID "577441".
- Compact_operator wikiPageLength "10669".
- Compact_operator wikiPageOutDegree "64".
- Compact_operator wikiPageRevisionID "683542414".
- Compact_operator wikiPageWikiLink Algebra_over_a_field.
- Compact_operator wikiPageWikiLink Approximation_property.
- Compact_operator wikiPageWikiLink Arzelà–Ascoli_theorem.
- Compact_operator wikiPageWikiLink Ascoli_theorem.
- Compact_operator wikiPageWikiLink Banach_space.
- Compact_operator wikiPageWikiLink Bounded_operator.
- Compact_operator wikiPageWikiLink Calkin_algebra.
- Compact_operator wikiPageWikiLink Category:Compactness_(mathematics).
- Compact_operator wikiPageWikiLink Category:Operator_theory.
- Compact_operator wikiPageWikiLink Cauchy_sequence.
- Compact_operator wikiPageWikiLink Compact_embedding.
- Compact_operator wikiPageWikiLink Compactly_embedded.
- Compact_operator wikiPageWikiLink Countable_set.
- Compact_operator wikiPageWikiLink Eigenvalue.
- Compact_operator wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Compact_operator wikiPageWikiLink Elliptic_boundary_value_problem.
- Compact_operator wikiPageWikiLink Equicontinuity.
- Compact_operator wikiPageWikiLink Finite-rank_operator.
- Compact_operator wikiPageWikiLink Fredholm_alternative.
- Compact_operator wikiPageWikiLink Fredholm_integral_equation.
- Compact_operator wikiPageWikiLink Fredholm_operator.
- Compact_operator wikiPageWikiLink Frigyes_Riesz.
- Compact_operator wikiPageWikiLink Function_space.
- Compact_operator wikiPageWikiLink Functional_analysis.
- Compact_operator wikiPageWikiLink Gxc3xa5rdings_inequality.
- Compact_operator wikiPageWikiLink Gårding_inequality.
- Compact_operator wikiPageWikiLink Hilbert-Schmidt_kernel.
- Compact_operator wikiPageWikiLink Hilbert_space.
- Compact_operator wikiPageWikiLink Hilbert–Schmidt_integral_operator.
- Compact_operator wikiPageWikiLink Ideal_(ring_theory).
- Compact_operator wikiPageWikiLink Identity_function.
- Compact_operator wikiPageWikiLink Identity_operator.
- Compact_operator wikiPageWikiLink Integral_equation.
- Compact_operator wikiPageWikiLink Kernel_(algebra).
- Compact_operator wikiPageWikiLink Lax–Milgram_theorem.
- Compact_operator wikiPageWikiLink Limit_point.
- Compact_operator wikiPageWikiLink Linear_map.
- Compact_operator wikiPageWikiLink Linear_operator.
- Compact_operator wikiPageWikiLink Mathematics.
- Compact_operator wikiPageWikiLink Neighbourhood_(mathematics).
- Compact_operator wikiPageWikiLink Nuclear_operator.
- Compact_operator wikiPageWikiLink Operator_norm.
- Compact_operator wikiPageWikiLink Per_Enflo.
- Compact_operator wikiPageWikiLink Quotient_algebra.
- Compact_operator wikiPageWikiLink Rank_(linear_algebra).
- Compact_operator wikiPageWikiLink Rank_of_a_linear_operator.
- Compact_operator wikiPageWikiLink Reflexive_Banach_space.
- Compact_operator wikiPageWikiLink Reflexive_space.
- Compact_operator wikiPageWikiLink Relatively_compact.
- Compact_operator wikiPageWikiLink Relatively_compact_subspace.
- Compact_operator wikiPageWikiLink Rieszs_lemma.
- Compact_operator wikiPageWikiLink Sequence.
- Compact_operator wikiPageWikiLink Sequence_(mathematics).
- Compact_operator wikiPageWikiLink Simple_algebra.
- Compact_operator wikiPageWikiLink Singular_value_decomposition.
- Compact_operator wikiPageWikiLink Sobolev_space.
- Compact_operator wikiPageWikiLink Spectral_theory_of_compact_operators.
- Compact_operator wikiPageWikiLink Strictly_singular.
- Compact_operator wikiPageWikiLink Strictly_singular_operator.
- Compact_operator wikiPageWikiLink Totally_bounded_space.
- Compact_operator wikiPageWikiLink Weak_formulation.
- Compact_operator wikiPageWikiLink Weak_topology.
- Compact_operator wikiPageWikiLinkText "Compact Operators".
- Compact_operator wikiPageWikiLinkText "Compact operator".
- Compact_operator wikiPageWikiLinkText "compact operator".
- Compact_operator wikiPageWikiLinkText "compact self-adjoint operator".
- Compact_operator wikiPageWikiLinkText "compact".
- Compact_operator wikiPageWikiLinkText "compactness".
- Compact_operator wikiPageWikiLinkText "strongly continuous".
- Compact_operator hasPhotoCollection Compact_operator.
- Compact_operator wikiPageUsesTemplate Template:Cite_book.
- Compact_operator wikiPageUsesTemplate Template:Functional_Analysis.
- Compact_operator wikiPageUsesTemplate Template:Harv.
- Compact_operator wikiPageUsesTemplate Template:Main.
- Compact_operator wikiPageUsesTemplate Template:Refimprove.
- Compact_operator subject Category:Compactness_(mathematics).
- Compact_operator subject Category:Operator_theory.
- Compact_operator hypernym L.
- Compact_operator type Article.
- Compact_operator type Person.
- Compact_operator type Article.
- Compact_operator type Physic.
- Compact_operator type Property.
- Compact_operator comment "In functional analysis, a branch of mathematics, a compact operator is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset of Y.".
- Compact_operator label "Compact operator".
- Compact_operator sameAs Operador_compacte.
- Compact_operator sameAs Kompakt_lineær_operator.
- Compact_operator sameAs Kompakter_Operator.
- Compact_operator sameAs Opérateur_compact.
- Compact_operator sameAs אופרטור_קומפקטי.
- Compact_operator sameAs Operatore_compatto.
- Compact_operator sameAs コンパクト作用素.
- Compact_operator sameAs 콤팩트_작용소.
- Compact_operator sameAs Operator_zwarty.
- Compact_operator sameAs Operador_compacto.