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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제60권 제3호
- 발행연도
- 2023.5
- 수록면
- 677 - 685 (9page)
- DOI
- 10.4134/BKMS.b220330
이용수
초록· 키워드
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For $n\geq 2$ and a real Banach space $E$, ${\mathcal L}(^n E:E)$ denotes the space of all continuous $n$-linear mappings from $E$ to itself. Let $$\Pi(E)=\{[x^*, (x_1, \ldots, x_n)]: x^{*}(x_j)=\|x^{*}\|=\|x_j\|=1~\mbox{for}~{j=1, \ldots, n}~\}.$$ An element $[x^*, (x_1, \ldots, x_n)]\in \Pi(E)$ is called a {\em numerical radius point} of $T\in {\mathcal L}(^n E:E)$ if $|x^{*}(T(x_1, \ldots, x_n))|=v(T)$, where the numerical radius $v(T)=\sup_{[y^*, y_1, \ldots, y_n]\in \Pi(E)}\Big|y^{*}\Big(T(y_1, \ldots,y_n)\Big)\Big|$. For $T\in {\mathcal L}(^n E:E)$, we define \begin{align*} \qopname\relax o{Nradius}({T})=&\ \{[x^*, (x_1, \ldots, x_n)]\in \Pi(E): [x^*, (x_1, \ldots, x_n)]\\ &\quad \mbox{is a numerical radius point of}~T\}. \end{align*} $T$ is called a {\em numerical radius peak $n$-linear mapping} if there is a unique $[x^{*}, (x_1, \ldots, x_n)]\in \Pi(E)$ such that $\qopname\relax o{Nradius}({T})=\{\pm [x^{*}, (x_1, \ldots, x_n)]\}$. In this paper we present explicit formulae for the numerical radius of $T$ for every $T\in {\mathcal L}(^n E:E)$ for $E=c_0$ or $l_{\infty}$. Using these formulae we show that there are no numerical radius peak mappings of ${\mathcal L}(^n c_0:c_0)$.
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