Geodesic
On the Stability of the Functional Quadratic on A-orthogonal Vectors
Publications de l'Institut Mathématique, _N_S_36 (1984) no. 50, p. 111

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Let $X$ be a complex Hilbert space ($\dim X $ is at least three) and $A$ a bounded selfadjoint operator on $X$ ($\dim AX $ is neither 1 nor 2). In this paper we study a continuous functional $h$ on $X$ which is approximately quadratic on $A$-orthogonal vectors (i.e., $(\alpha_1)$ is satisfied provided that $(Ax,y)=0$). We find that there exists a unique continuous functional $h_1$ (given by ($\alpha_2$)) which is quadratic on $A$-orthogonal vectors (i.e., $(\alpha_3)$ holds) and which is near $h$ (i.e., $(\alpha_4)$ holds).
Classification : 65L07 
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     author = {Hamid Drljevi\'c},
     title = {On the {Stability} of the {Functional} {Quadratic} on {A-orthogonal} {Vectors}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {111 },
     publisher = {mathdoc},
     volume = {_N_S_36},
     number = {50},
     year = {1984},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a17/}
}
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Hamid Drljević. On the Stability of the Functional Quadratic on A-orthogonal Vectors. Publications de l'Institut Mathématique, _N_S_36 (1984) no. 50, p. 111 . http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a17/