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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.".
- Compact_operator_on_Hilbert_space wikiPageID "6690773".
- Compact_operator_on_Hilbert_space wikiPageRevisionID "598771860".
- Compact_operator_on_Hilbert_space hasPhotoCollection Compact_operator_on_Hilbert_space.
- 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 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 label "ヒルベルト空間上のコンパクト作用素".
- 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=598771860.
- Compact_operator_on_Hilbert_space isPrimaryTopicOf Compact_operator_on_Hilbert_space.