Abstract
Sometimes we have to deal with equations (A) such that one can see from their structure immediately that they cannot be solved for all y ∈ F. For example, this happens if there is a closed operator Φ, acting from F into another Banach space G, and such that ΦA = 0. Then equation Ax = y can be solved only for y ∈ N(Φ). Relative to a given pair of spaces E and F, an equation which can be solved only when the right-hand side is contained in a subspace F, of F, must be naturally considered as overdetermined.
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© 1982 Birkhäuser Boston, Inc.
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Krein, S.G. (1982). Overdetermined Equations. In: Linear Equations in Banach Spaces. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-8068-9_17
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DOI: https://doi.org/10.1007/978-1-4684-8068-9_17
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3101-7
Online ISBN: 978-1-4684-8068-9
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