Let X be an infinite-dimensional Banach space, and B(X) the algebra of all bounded linear operators on X. Then ϕ: B(X) → B(X) is a bijective similarity-preserving linear map if and only if one of the following holds: (1) There exist a nonzero complex number c, an invertible bounded operator T in B(X) and a similarity-invariant linear functional h on B(X) with h(I) ≠ -c such that for all A ∈ B(X). (2) There exist a nonzero complex number c, an invertible bounded linear operator T: X* → X and a similarity-invariant linear functional h on B(X) with h(I) ≠ -c such that for all A ∈ B(X).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-1-1,
author = {Fangyan Lu and Chaoran Peng},
title = {Similarity-preserving linear maps on B(X)},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {1-10},
zbl = {1254.47027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-1-1}
}
Fangyan Lu; Chaoran Peng. Similarity-preserving linear maps on B(X). Studia Mathematica, Tome 209 (2012) pp. 1-10. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-1-1/