Document Type

Article

Date

10-1-2009

Embargo Period

11-28-2011

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.

Additional Information

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

Source

Harvested from arXiv.org

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

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