Geodesic
Two characterizations of automorphisms on B(X)
Studia Mathematica, Tome 105 (1993) no. 2, pp. 143-149 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let X be an infinite-dimensional Banach space, and let ϕ be a surjective linear map on B(X) with ϕ(I) = I. If ϕ preserves injective operators in both directions then ϕ is an automorphism of the algebra B(X). If X is a Hilbert space, then ϕ is an automorphism of B(X) if and only if it preserves surjective operators in both directions. 
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     author = {Peter \v{S}emrl},
     title = {Two characterizations of automorphisms on {B(X)}},
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Peter Šemrl. Two characterizations of automorphisms on B(X). Studia Mathematica, Tome 105 (1993) no. 2, pp. 143-149. doi: 10.4064/sm-105-2-143-149

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