Similarity-preserving linear maps on B(X)

Fangyan Lu, and Chaoran Peng. "Similarity-preserving linear maps on B(X)." Studia Mathematica 209.1 (2012): 1-10. <http://eudml.org/doc/285727>.

@article{FangyanLu2012,
abstract = {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 $ϕ(A) = cTAT^\{-1\} + h(A)I$ 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 $ϕ(A) = cTA*T^\{-1\} + h(A)I$ for all A ∈ B(X).},
author = {Fangyan Lu, Chaoran Peng},
journal = {Studia Mathematica},
keywords = {Banach spaces; similar operators; similarity-preserving maps; similarity-invariant functionals},
language = {eng},
number = {1},
pages = {1-10},
title = {Similarity-preserving linear maps on B(X)},
url = {http://eudml.org/doc/285727},
volume = {209},
year = {2012},
}

TY - JOUR
AU - Fangyan Lu
AU - Chaoran Peng
TI - Similarity-preserving linear maps on B(X)
JO - Studia Mathematica
PY - 2012
VL - 209
IS - 1
SP - 1
EP - 10
AB - 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 $ϕ(A) = cTAT^{-1} + h(A)I$ 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 $ϕ(A) = cTA*T^{-1} + h(A)I$ for all A ∈ B(X).
LA - eng
KW - Banach spaces; similar operators; similarity-preserving maps; similarity-invariant functionals
UR - http://eudml.org/doc/285727
ER -