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RISS 인기검색어
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- 저자 : Ramesh Golla (검색결과 2 건)
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Linear maps preserving AN-operators
Ramesh Golla,Hiroyuki Osaka 대한수학회 2020 대한수학회보 Vol.57 No.4
Let $H$ be a complex Hilbert space and $T : H\rightarrow H$ be a bounded linear operator. Then $T$ is said to be \textit{norm attaining} if there exists a unit vector $x_0\in H$ such that $\|Tx_0\|=\|T\|$. If for any closed subspace $M$ of $H$, the restriction $T|M : M \rightarrow H$ of $T$ to $M$ is norm attaining, then $T$ is called an \textit{absolutely norm attaining} operator or $\mathcal{AN}$-operator. In this note, we discuss linear maps on $\mathcal B(H)$, which preserve the class of absolutely norm attaining operators on $H$.
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LINEAR MAPS PRESERVING 𝓐𝓝-OPERATORS
Golla, Ramesh,Osaka, Hiroyuki Korean Mathematical Society 2020 대한수학회보 Vol.57 No.4
Let H be a complex Hilbert space and T : H → H be a bounded linear operator. Then T is said to be norm attaining if there exists a unit vector x<sub>0</sub> ∈ H such that ║Tx<sub>0</sub>║ = ║T║. If for any closed subspace M of H, the restriction T|M : M → H of T to M is norm attaining, then T is called an absolutely norm attaining operator or 𝓐𝓝-operator. In this note, we discuss linear maps on B(H), which preserve the class of absolutely norm attaining operators on H.
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