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- Compact_operator_on_Hilbert_space abstract "In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite-rank operators in the uniform operator topology. As such, results from matrix theory can sometimes be extended to compact operators using similar arguments. In contrast, the study of general operators on infinite-dimensional spaces often requires a genuinely different approach.For example, the spectral theory of compact operators on Banach spaces takes a form that is very similar to the Jordan canonical form of matrices. In the context of Hilbert spaces, a square matrix is unitarily diagonalizable if and only if it is normal. A corresponding result holds for normal compact operators on Hilbert spaces. (More generally, the compactness assumption can be dropped. But, as stated above, the techniques used are less routine.)This article will discuss a few results for compact operators on Hilbert space, starting with general properties before considering subclasses of compact operators.".
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- Compact_operator_on_Hilbert_space wikiPageOutDegree "43".
- Compact_operator_on_Hilbert_space wikiPageRevisionID "618921496".
- Compact_operator_on_Hilbert_space wikiPageWikiLink Banach_space.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Banach–Alaoglu_theorem.
- Compact_operator_on_Hilbert_space wikiPageWikiLink C*-algebra.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Calkin_algebra.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Category:Articles_containing_proofs.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Category:Hilbert_space.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Category:Operator_theory.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Compact_operator.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Continuous_functional_calculus.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Countable_set.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Decomposition_of_spectrum_(functional_analysis).
- Compact_operator_on_Hilbert_space wikiPageWikiLink Direct_sum.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Finite-rank_operator.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Functional_analysis.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Functional_calculus.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Hilbert_space.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Hilbert–Schmidt_operator.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Hyponormal_operator.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Jordan_canonical_form.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Jordan_normal_form.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Kernel_(linear_algebra).
- Compact_operator_on_Hilbert_space wikiPageWikiLink Kernel_(linear_operator).
- Compact_operator_on_Hilbert_space wikiPageWikiLink Lagrange_multiplier.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Lagrange_multipliers.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Lp_space.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Mercers_theorem.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Normal_operator.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Operator_topologies.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Operator_topology.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Orthogonal_complement.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Orthonormal_basis.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Polarization_identity.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Rayleigh_quotient.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Relatively_compact_subspace.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Self-adjoint_operator.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Separable_space.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Singular_value_decomposition.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Spectral_theorem.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Spectral_theory_of_compact_operators.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Stone–Weierstrass_theorem.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Strong_operator_topology.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Subnormal_operator.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Unitary_operator.
- Compact_operator_on_Hilbert_space wikiPageWikiLink Weak_convergence_(Hilbert_space).
- Compact_operator_on_Hilbert_space wikiPageWikiLink Zorns_lemma.
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "Compact operator on Hilbert space".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "Compact operators on a Hilbert space".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "compact normal operator".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "compact operator on Hilbert space".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "compact operator".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "compact operators on a separable Hilbert space".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "compact operators".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "compact self-adjoint operator".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "compact".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "spectral theorem for compact operators".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "spectral theorem for compact self-adjoint operators".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "spectral theorem".
- Compact_operator_on_Hilbert_space wikiPageWikiLinkText "spectral theory".
- Compact_operator_on_Hilbert_space hasPhotoCollection Compact_operator_on_Hilbert_space.
- Compact_operator_on_Hilbert_space wikiPageUsesTemplate Template:=.
- Compact_operator_on_Hilbert_space wikiPageUsesTemplate Template:Citation.
- Compact_operator_on_Hilbert_space wikiPageUsesTemplate Template:Harv.
- Compact_operator_on_Hilbert_space subject Category:Articles_containing_proofs.
- Compact_operator_on_Hilbert_space subject Category:Hilbert_space.
- Compact_operator_on_Hilbert_space subject Category:Operator_theory.
- Compact_operator_on_Hilbert_space hypernym Extension.
- Compact_operator_on_Hilbert_space type Article.
- Compact_operator_on_Hilbert_space type Software.
- Compact_operator_on_Hilbert_space type Article.
- Compact_operator_on_Hilbert_space type Mechanic.
- Compact_operator_on_Hilbert_space type Physic.
- Compact_operator_on_Hilbert_space type Proof.
- Compact_operator_on_Hilbert_space type Space.
- Compact_operator_on_Hilbert_space comment "In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite-rank operators in the uniform operator topology. As such, results from matrix theory can sometimes be extended to compact operators using similar arguments.".
- Compact_operator_on_Hilbert_space label "Compact operator on Hilbert space".
- Compact_operator_on_Hilbert_space sameAs ヒルベルト空間上のコンパクト作用素.
- Compact_operator_on_Hilbert_space sameAs m.0ghh7h.
- Compact_operator_on_Hilbert_space sameAs Q5155314.
- Compact_operator_on_Hilbert_space sameAs Q5155314.
- Compact_operator_on_Hilbert_space wasDerivedFrom Compact_operator_on_Hilbert_space?oldid=618921496.
- Compact_operator_on_Hilbert_space isPrimaryTopicOf Compact_operator_on_Hilbert_space.