#### Document Type

Article

#### Date

10-1-2009

#### Disciplines

Mathematics

#### Description/Abstract

Let B(X) be the algebra of all bounded linear operators on an infinite dimensional complex Banach space X. We prove that an additive surjective map phi on B(X) preserves the reduced minimum modulus if and only if either there are bijective isometries U:X -> X and V:X -> X both linear or both conjugate linear such that phi(T)=UTV for all T in B(X), or X is reflexive and there are bijective isometries U:X^{* }-> X and V:X -> X^{*} both linear or both conjugate linear such that phi(T)=UT^{*}V for all T in B(X). As immediate consequences of the ingredients used in the proof of this result, we get the complete description of surjective additive maps preserving the minimum, the surjectivity and the maximum moduli of Banach space operators.

#### Recommended Citation

Bourhim, Abdellatif, "Additive Maps Preserving the Reduced Minimum Modulus of Banach Space Operators" (2009). *Mathematics Faculty Scholarship*. 88.

https://surface.syr.edu/mat/88

#### Source

Harvested from arXiv.org

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.

## Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/0910.0283