Kyungpook Mathematical Journal

  • 제53권1호
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  • Pages.117-124
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  • 2013
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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The Polynomial Numerical Index of Lp(μ)

  • Kim, Sung Guen (Department of Mathematics, Kyungpook National University)
  • 투고 : 2012.07.11
  • 심사 : 2012.08.23
  • 발행 : 2013.03.23
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초록

We show that for 1 < $p$ < ${\infty}$, $k$, $m{\in}\mathbb{N}$, $n^{(k)}(l_p)=inf\{n^{(k)}(l^m_p):m{\in}\mathbb{N}\}$ and that for any positive measure ${\mu}$, $n^{(k)}(L_p({\mu})){\geq}n^{(k)}(l_p)$. We also prove that for every $Q{\in}P(^kl_p:l_p)$ (1 < $p$ < ${\infty}$), if $v(Q)=0$, then ${\parallel}Q{\parallel}=0$.

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과제정보

연구 과제 주관 기관 : National Research Foundation of Korea(NRF)

참고문헌

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  10. S. G. Kim, M. Martin and J. Meri, On the polynomial numerical index of the real spaces $c_0$, $\ell_1$, ${\ell}_{\infty}$, J. Math. Anal. Appl., 337 (2008), 98-106. https://doi.org/10.1016/j.jmaa.2007.03.101
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피인용 문헌

  1. Generalized Numerical Index and Denseness of Numerical Peak Holomorphic Functions on a Banach Space vol.2013, 2013, https://doi.org/10.1155/2013/380475