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On the representation of functionals and the stability of mappings in Hilbert and Banach spaces. (English) Zbl 0752.47014

Topics in mathematical analysis, Vol. Dedicated Mem. of A. L. Cauchy, Ser. Pure Math. 11, 231-245 (1989).
Summary: [For the entire collection see Zbl 0721.00014.]
We will present:
I. A brief historical review of the representation of functionals or of operators.
II. A brief historical review of the stability of functionals or of operators.
III. A sketch of the proof of the theorem about representation in Hilbert space which is quadratic on \(A\)-orthogonal pairs.
I do not pretend to present complete results discussed in I and II, and will present only the results accessible to the authors at the moment this paper was written.

MSC:

47B60 Linear operators on ordered spaces
46A40 Ordered topological linear spaces, vector lattices

Biographic References:

Cauchy, A. L.

Citations:

Zbl 0721.00014
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