ADDITIVE MAPS PRESERVING THE REDUCED MINIMUM MODULUS OF BANACH SPACE OPERATORS

作者：Bourhim Abdellatif^*

来源：Journal of Operator Theory, 2012, 67(1): 279-288.

• Linear and additive preservers
• reduced minimum modulus
• minimum modulus
• surjectivity modulus

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 isometrics U : X -%26gt; X and V : X -%26gt; X both linear or both conjugate linear such that phi(T) = UTV for all T is an element of B(X), or X is reflexive and there are bijective isometrics U : X* -%26gt; X and V : X -%26gt; X* both linear or both conjugate linear such that phi(T) = UT*V for all T is an element of 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.

• 出版日期2012