Examples of Compactness

  • Paul R. Halmos
Part of the Graduate Texts in Mathematics book series (GTM, volume 19)


Integral operators are generalized matrices. Experience with matrices shows that the more zeros they have, the easier they are to compute with; triangular matrices, in particular, are usually quite tractable. Which integral operators are the right generalizations of triangular matrices? For the answer it is convenient to specialize drastically the measure spaces considered; in what follows the only X will be the unit interval, and the only μ will be Lebesgue measure. (The theory can be treated somewhat more generally; see [115].)


Invariant Subspace Triangular Matrix Triangular Matrice Volterra Operator Volterra Kernel 
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© Springer-Verlag New York Inc 1982

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  • Paul R. Halmos

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