A note on the Hyers--Ulam stability constants of closed linear operators

Qianglian Huang, Lanping Zhu, Bo Wu


This paper concerns the properties of the Hyers--Ulam stability constant of closed linear operators. Using the Moore-Penrose inverse, we prove that the mapping $\overline{T}\rightarrow K_{\overline{T}}$ is lower semi-continuous and give some sufficient and necessary conditions for $\overline{T}\rightarrow K_{\overline{T}}$ to be continuous or locally bounded.}
\par\noindent{\bf{\it Keywords}}: the constant of the Hyers--Ulam stability; Moore--Penrose inverse; lower semi-continuity; continuity; local boundedness.

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