Adjoint Subspaces in Banach Spaces, with Applications to Ordinary Differential Subspaces

Earl A. Coddington*, Aalt Dijksma

*Bijbehorende auteur voor dit werk

    OnderzoeksoutputAcademicpeer review

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    Given two subspaces A0 ⊂ A1 ⊂ W = X ⊕ Y, where X, Y are Banach spaces, we show how to characterize, in terms of generalized boundary conditions, those adjoint pairs A, A* satisfying A0 ⊂ A ⊂ A1, A1* ⊂ A* ⊂ A0* ⊂ W+ = Y* ⊕ X*, where X*, Y* are the conjugate spaces of X, Y, respectively. The characterizations of selfadjoint (normal) subspace extensions of symmetric (formally normal) subspaces appear as special cases when Y = X*. These results are then applied to ordinary differential subspaces in W = Lq(ι) ⊕ Lr(ι), 1 ≤ q, r ≤ ∞, where ι is a real interval, and in W = C(ī) ⊕ C(ī), where ī is a compact interval.
    Originele taal-2English
    Aantal pagina's118
    TijdschriftAnnali di Matematica Pura ed Applicata
    Volume118
    Nummer van het tijdschrift1
    StatusPublished - 1978

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