Some Properties of Closed Range Operators

J. Farokhi-Ostad; M.H. Rezaei-Gol

doi:https://doi.org/10.14445/22315373/IJMTT-V38P530

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 38 | Number 3 | Year 2016 | Article Id. IJMTT-V38P530 | DOI : https://doi.org/10.14445/22315373/IJMTT-V38P530

Some Properties of Closed Range Operators

J. Farokhi-Ostad, M.H. Rezaei-Gol

Abstract

For the two bounded adjointable operators T and S with close ranges on Hilbert A-modules, we demonstrate that, T S has closed range if and only if ker(T) + ran(S) be an orthogonal summand. Also, we conclude that T S has closed range if and only if ker(S ∗ ) + ran(T ∗ ) be an orthogonal summand. In addition we investigate the equivalence conditions for close range operators.

Keywords

Hilbert A-module, projection, closed range, complemented submodules.

References

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Citation :

J. Farokhi-Ostad, M.H. Rezaei-Gol, "Some Properties of Closed Range Operators," International Journal of Mathematics Trends and Technology (IJMTT), vol. 38, no. 3, pp. 172-179, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V38P530