Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Polynomial Numerical Index of Lp(μ)

  • Kim, Sung Guen (Department of Mathematics, Kyungpook National University)
  • Received : 2012.07.11
  • Accepted : 2012.08.23
  • Published : 2013.03.23
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Abstract

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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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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  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