• Title, Summary, Keyword: parallelogram law

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CHARACTERIZATIONS OF AN INNER PRODUCT SPACE BY GRAPHS

  • Lin, C.S.
    • The Pure and Applied Mathematics
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    • v.16 no.4
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    • pp.359-367
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    • 2009
  • The graph of the parallelogram law is well known, which gives rise to the characterization of an inner product space among normed linear spaces [6]. In this paper we will sketch graphs of its deformations according to our previous paper [7, Theorem 3.1 and 3.2]; each one of which characterizes an inner product space among normed linear spaces. Consequently, the graphs of some classical characterizations of an inner product space follow easily.

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BOHR'S INEQUALITIES IN n-INNER PRODUCT SPACES

  • Cheung, W.S.;Cho, Y.S.;Pecaric, J.;Zhao, D.D.
    • The Pure and Applied Mathematics
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    • v.14 no.2
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    • pp.127-137
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    • 2007
  • The classical Bohr's inequality states that $|z+w|^2{\leq}p|z|^2+q|w|^2$ for all $z,\;w{\in}\mathbb{C}$ and all p, q>1 with $\frac{1}{p}+\frac{1}{q}=1$. In this paper, Bohr's inequality is generalized to the setting of n-inner product spaces for all positive conjugate exponents $p,\;q{\in}\mathbb{R}$. In. In particular, the parallelogram law is recovered and an interesting operator inequality is obtained.

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