Adjoint subspaces in Banach spaces,with applications to ordinary differential subspaces |
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Authors: | Earl A. Coddington Aalt Dijksma |
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Affiliation: | (1) Los Angeles, Cal., U.S.A.;(2) Groningen, Netherlands |
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Abstract: | Summary 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, A 1 * ⊂ A∗ ⊂ A 0 * ⊂ 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 τ is a real interval, and in W=C( ) ⊕ C( ), where is a compact interval. Entrata in Redazione il 21 febbraio 1977. The work of EarlA. Coddington was supported in part by the National Science Foundation under NSF Grant No. MCS-76-05855. |
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