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Local derivations and local automorphisms of B(X)
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Isometries of norm ideals of compact operators
Abstract Let J be a symmetric norm ideal of compact operators on Hilbert space H , and assume that the finite rank operators are dense in J and that J is not the ideal of Hilbert-Schmidt operators. AExpand
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A factorization theorem for matrices
It is shown that a nonscalar invertible square matrix can be written as a product of two square matrices with prescribed eigenvalues subject only to the obvious determinant condition. As corollaries,Expand
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INVERTIBILITY PRESERVING LINEAR MAPS ON L(X)
For Banach spaces X and Y , we show that every unital bijective invertibility preserving linear map between L(X) and L(Y ) is a Jordan isomorphism. The same conclusion holds for maps between CI +Expand
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Lie and Jordan ideals of operators on Hilbert space
A linear manifold 2 in ©(§) is a Lie ideal in 33(§) if and only if there is an associative ideal 5 such that (S. ^(C)) C 2 c S + CI. Also S is a Lie ideal if and only if it contains the unitary orbitExpand
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Additive rank-one preserving mappings on triangular matrix algebras
Abstract We classify surjective additive maps on the space of block upper triangular matrices that preserve matrices of rank one as well as linear maps preserving matrices of rank one on fairlyExpand
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Sums and products of quasi-nilpotent operators
It is proved that a bounded operator on Hilbert space is the sum of two quasi-nilpotent operators if and only if it is not a non-zero scalar plus a compact operator. Necessary conditions andExpand
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LIE ISOMORPHISMS OF NEST ALGEBRAS
Abstract In this paper we characterize linear maps ϕ between two nest algebras T ( N ) and T ( M ) which satisfy the property that ϕ ( AB − BA )= ϕ ( A )  ϕ ( B )− ϕ ( B )  ϕ ( A ) for all A ,  B ∈ TExpand
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Spectrum-preserving linear maps
Abstract Let X and Y be Banach spaces. We show that a spectrum preserving surjective linear map φ from B ( X ) to B ( Y ) is either of the form φ ( T ) = ATA −1 for an isomorphism A of X onto Y orExpand
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SPECTRAL PROPERTIES OF THE OPERATOR EQUATION AX + XB = Y
(under the assumption o(A) =£ C or o(B) =£ C), so that 0 £ o(A) + o(B) is a necessary condition for existence and uniqueness of (0.1). The proof of (0.3) we give in Section 2 seems to be new even forExpand
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