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Fichera's existence principle

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In mathematics, and particularly in functional analysis, Fichera's existence principle is an existence and uniqueness theorem for solution of functional equations, proved by Gaetano Fichera in 1954.[1] More precisely, given a general vector space V and two linear maps from it onto two Banach spaces, the principle states necessary and sufficient conditions for a linear transformation between the two dual Banach spaces to be invertible for every vector in V.[2]

See also

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Notes

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  1. ^ (Faedo 1957, p. 1), (Valent 1999, p. 84), (Leonardi, Passarelli di Napoli & Sbordone 2000, p. 221).
  2. ^ See (Fichera 1955, pp. 175–177, 1958, pp. 30–35), (Faedo 1957, pp. 1–2), (Miranda 1970, pp. 123–124), (Valent 1999, p. 84).

References

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