ALMOST REGULAR OPERATORS ARE REGULAR

Abstract

We give a characterization of regular operators that allows us to prove that a bounded operator acting between Banach spaces is almost regular if and only if it is regular, solving an open problem in [5]. As an application, we show that some operators in the closure of the set of all regular operators are regular.

Keywords

• almost regular operator;
• regular operator

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References

1. Unbounded linear operators S.Goldberg
2. Bollenttino U.M.I. v.11-B Ultrapowers and semi-Fredholm operators M.Gonzalez;A.marinez-Abejon
3. Invertibility and singularity for bounded linear operators R.Harte
4. J. Reine Angew. Math. v.313 Ultraproducts in Banach space theory S.Heinrich
5. J. Korean Math. Soc. v.29 Almost regular operators Woo Young Lee;Chun In Choi