EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 36(50), pp. 111--118 (1984)

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ON THE STABILITY OF THE FUNCTIONAL QUADRATIC ON $A$-ORTHOGONAL VECTORS

Hamid Drljevi\'c

Ekonomski 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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Electronic fulltext finalized on: 3 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
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