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HYERS-ULAM STABILITY OF A CLOSED OPERATOR IN A HILBERT SPACE
Hirasawa Go,Miura Takeshi Korean Mathematical Society 2006 대한수학회보 Vol.43 No.1
We give some necessary and sufficient conditions in order that a closed operator in a Hilbert space into another have the Hyers-Ulam stability. Moreover, we prove the existence of the stability constant for a closed operator. We also determine the stability constant in terms of the lower bound.
Hyers-Ulam stability of a closed operator in a Hilbert space
Go Hirasawa,Takeshi Miura 대한수학회 2006 대한수학회보 Vol.43 No.1
sufficient conditions in order that a closed operator in a Hilbertspace into another have the Hyers-Ulam stability. Moreover, weprove the existence of the stability constant for a closedoperator. We also determine the stability constant in terms of the lower bound.
A perturbation of ring derivations on Banach algebras
Miura, Takeshi,Hirasawa, Go,Takahasi, Sin-Ei Elsevier 2006 Journal of mathematical analysis and applications Vol.319 No.2
<P><B>Abstract</B></P><P>Suppose <I>A</I> is a Banach algebra and suppose f:A→A is an approximate ring derivation in the sense of Hyers–Ulam–Rassias. This stability phenomenon was introduced for the first time in the subject of functional equations by Th.M. Rassias [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297–300]. If <I>A</I> has an approximate identity, or if <I>A</I> is semisimple and commutative, then we prove that <I>f</I> is an exact ring derivation.</P>