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Similarity-preserving linear maps on B(X)

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Lu F., Peng C.

Studia Mathematica

2012

tom 209

nr 1

1-10

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).

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1 Studia Mathematica

1 Lu F.

1 Peng C.

1 2012

Wyniki wyszukiwania

Similarity-preserving linear maps on B(X)