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Compact operator

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  1. 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 i

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 29, 2008
  2. a linear operator that takes bounded subsets to relatively compact subsets, in functional analysis

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 29, 2008
  3. Any L that has finite rank is a compact operator

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 29, 2008
  4. When X = Y and 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

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 29, 2008
  5. indeed, the class of compact operators is a natural generalisation of the class of finite rank operators in an infinite-dimensional setting

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 29, 2008
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