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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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참고문헌 (11)
참고문헌 신청
Xavier Carvajal / 2012 / Operators That Achieve the Norm / Integral Equations and Operator Theory 72(2):179~195
Xavier Carvajal / 2014 / Operators that attain their minima / Bulletin of the Brazilian Mathematical Society, New Series 45(2):293~312
Ganesh J. / 2018 / A characterization of absolutely minimum attaining operators / Journal of Mathematical Analysis and Applications 468(1):567~583
Máté Györy / 1998 / Linear rank and corank preserving maps on B(H) and an application to ∗-semigroup isomorphisms of operator ideals / Linear Algebra and its Applications 280(2-3):253~266
J. -C. Hou / 1998 / A characterization of positive elementary operators / J. Operator Theory 39(1):43~58
Xavier Carvajal / 2014 / Operators that attain their minima / Bulletin of the Brazilian Mathematical Society, New Series 45(2):293~312
Ganesh J. / 2018 / A characterization of absolutely minimum attaining operators / Journal of Mathematical Analysis and Applications 468(1):567~583
Máté Györy / 1998 / Linear rank and corank preserving maps on B(H) and an application to ∗-semigroup isomorphisms of operator ideals / Linear Algebra and its Applications 280(2-3):253~266
J. -C. Hou / 1998 / A characterization of positive elementary operators / J. Operator Theory 39(1):43~58
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