Premium
Coordinatized Adjoint Subspaces in Hilbert Spaces, with Application to Ordinary Differential Operators
Author(s) -
Lee Sung J.
Publication year - 1980
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-41.1.138
Subject(s) - mathematics , linear subspace , hilbert space , pure mathematics , linear operators , closed set , closed manifold , differential operator , boundary (topology) , extension (predicate logic) , operator (biology) , manifold (fluid mechanics) , linear map , ordinary differential equation , mathematical analysis , invariant manifold , differential equation , mechanical engineering , biochemistry , chemistry , repressor , computer science , transcription factor , engineering , bounded function , gene , programming language
Let T 0 ⊂ T 1 be a closed linear manifold in the direct sum H 1 ⊕ H 2 of Hilbert spaces such that dim T 1 / T 0 is at most countably infinite. We characterize any closed linear manifold between T 0 and T 1 and its adjoint subspace in terms of a given set of abstract boundary conditions. In particular, we generalize the extension theory of closed symmetric operator discussed by Dunford and Schwartz [6]. An application is given to the closed linear manifolds which are generated by countably many ordinary linear differential expressions with matrix coefficients.