Maps preserving general means of positive operators

Under some mild conditions, the general form of bijective transformations of the set of all positive linear operators on a Hilbert space which preserve a symmetric mean in the sense of Kubo-Ando theory is described.

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Ela Maps Preserving General Means of Positive Operators∗

Under some mild conditions, the general form of bijective transformations of the set of all positive linear operators on a Hilbert space which preserve a symmetric mean in the sense of Kubo-Ando theory is described.

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Maps on positive operators preserving Lebesgue decompositions

Let H be a complex Hilbert space. Denote by B(H)+ the set of all positive bounded linear operators on H. A bijective map φ : B(H)+ → B(H)+ is said to preserve Lebesgue decompositions in both directions if for any quadruple A,B,C,D of positive operators, B = C +D is an A-Lebesgue decomposition of B if and only if φ(B) = φ(C)+φ(D) is a φ(A)-Lebesgue decomposition of φ(B). It is proved that every ...

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Ela Maps on Positive Operators Preserving

Let H be a complex Hilbert space. Denote by B(H)+ the set of all positive bounded linear operators on H. A bijective map φ : B(H)+ → B(H)+ is said to preserve Lebesgue decompositions in both directions if for any quadruple A,B,C,D of positive operators, B = C +D is an A-Lebesgue decomposition of B if and only if φ(B) = φ(C)+φ(D) is a φ(A)-Lebesgue decomposition of φ(B). It is proved that every ...

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Additive Maps Preserving Idempotency of Products or Jordan Products of Operators

Let $mathcal{H}$ and $mathcal{K}$ be infinite dimensional Hilbert spaces, while $mathcal{B(H)}$ and $mathcal{B(K)}$ denote the algebras of all linear bounded operators on $mathcal{H}$ and $mathcal{K}$, respectively. We characterize the forms of additive mappings from $mathcal{B(H)}$ into $mathcal{B(K)}$ that preserve the nonzero idempotency of either Jordan products of operators or usual produc...

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Maps preserving general means of positive operators

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