PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 36(50), pp. 111--118 (1984)
ON THE STABILITY OF THE FUNCTIONAL QUADRATIC ON $A$-ORTHOGONAL VECTORS
Hamid Drljevi\'cEkonomski fakultet, Mostar Jugoslavija
Abstract: 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 (MSC2000): 65L07
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