• Title, Summary, Keyword: essential norm

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NORM AND ESSENTIAL NORM ESTIMATES OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

  • Choe, Boo-Rim;Lee, Young-Joo
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.937-958
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    • 1996
  • On the setting of product of balls we consider Toeplitz operators, with symbols satisfying a certain condition, on the Bergman space. Norms and essential norms of such operators are estimated by means of certain integral quantities.

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ESSENTIAL NORM OF THE COMPOSITION OPERATORS BETWEEN BERGMAN SPACES OF LOGARITHMIC WEIGHTS

  • Kwon, Ern Gun;Lee, Jinkee
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.1
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    • pp.187-198
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    • 2017
  • We obtain some necessary and sufficient conditions for the boundedness of the composition operators between weighted Bergman spaces of logarithmic weights. In terms of the conditions for the boundedness, we compute the essential norm of the composition operators.

A NOTE OF WEIGHTED COMPOSITION OPERATORS ON BLOCH-TYPE SPACES

  • LI, SONGXIAO;ZHOU, JIZHEN
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1711-1719
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    • 2015
  • We obtain a new criterion for the boundedness and compactness of the weighted composition operators ${\psi}C_{\varphi}$ from ${\ss}^{{\alpha}}$(0 < ${\alpha}$ < 1) to ${\ss}^{{\beta}}$ in terms of the sequence $\{{\psi}{\varphi}^n\}$. An estimate for the essential norm of ${\psi}C_{\varphi}$ is also given.

Some properties of equivalent fuzzy norms

  • Rhie, Gil-Seob;Hwang, In-Ah
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.5 no.2
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    • pp.175-178
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    • 2005
  • In the present paper, we observe a relation between fuzzy norms and induced crisp norms on a linear space. We first prove that if $\rho_1,\;\rho_2$ are equivalent fuzzy norms on a linear space, then for every $\varepsilon\in(0.1)$, the induced crisp norms $P_\varepsilon^1,\;and\;P_\varepsilon^2$, respectively are equivalent. Since the converse does not hold, we prove it under some strict conditions. And consider the following theorem proved in [8]: Let $\rho$ be a lower semicontinuous fuzzy norm on a normed linear space X, and have the bounded support. Then $\rho$ is equivalent to the fuzzy norm $\chi_B$ where B is the closed unit ball of X. The lower semi-continuity of $\rho$ is an essential condition which guarantees the continuity of $P_\varepsilon$, where 0 < e < 1. As the last result, we prove that : if $\rho$ is a fuzzy norm on a finite dimensional vector space, then $\rho$ is equivalent to $\chi_B$ if and only if the support of $\rho$ is bounded.

A NOTE ON OPERATORS ON FINSLER MODULES

  • TAGHAVI, A.;JAFARZADEH, JAFARZADEH
    • Honam Mathematical Journal
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    • v.28 no.4
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    • pp.533-541
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    • 2006
  • let E be a Finsler modules over $C^*$-algebras. A with norm-map $\rho$ and L(E) set of all A-linear bonded operators on E. We show that the canonical homomorphism ${\phi}:L(E){\rightarrow}L(E_I)$ sending each operator T to its restriction $T|E_I$ is injective if and only if I is an essential ideal in the underlying $C^*$-algebra A. We also show that $T{\in}L(E)$ is a bounded below if and only if ${\mid}{\mid}x{\mid}{\mid}={\mid}{\mid}{\rho}{\prime}(x){\mid}{\mid}$ is complete, where ${\rho}{\prime}(x)={\rho}(Tx)$ for all $x{\in}E$. Also, we give a necessary and sufficient condition for the equivalence of the norms generated by the norm map.

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A Study on Effects of Cyperus rotundus L. Essential Oil Inhalation on Stress Relaxation with HRV, EEG (향부자 정유 흡입이 스트레스 이완에 미치는 영향)

  • Uhm, Ji-Tae;Bae, Seon Young;Park, Kil-Soon;Kim, Kyoung-Shin
    • Journal of Haehwa Medicine
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    • v.22 no.2
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    • pp.81-92
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    • 2014
  • Objective : The purpose of this study was to assess the effects of Cyperus rotundus L. essential oil on relaxation in highly stressed volunteers with heart rate variability(HRV) and electroencephalography(EEG). Methods : 11 highly stressed volunteers participated in this study. The volunteers were examined with HRV and EEG before and after inhalation of Cyperus rotundus L. essential oil. Results : After smelling Cyperus rotundus L. essential oil, mean RR(mean of RR intervals) was incresed significantly(p<0.01), mean HRV(mean of heart rate), HF(high frequency) were decreased significantly(p<0.01). norm LF(low frequency), LF/HF ratio were decreased significantly(p<0.05), norm HF(normalized high frequency) was increased significantly(p<0.05) on HRV. After smelling Cyperus rotundus L. essential oil, relative ${\theta}$ power was decreased significantly(p<0.05) at P3(left parietal) and relative ${\alpha}$ power was increased significantly(p<0.05) at Fp1(left prefrontal), Fp2(right prefrontal) and relative ${\beta}$ power was decreased significantly(p<0.05) at Fp1(left prefrontal) and relative ${\gamma}$ power was decreased significantly(p<0.05) at Fp1(left prefrontal) on EEG. Conclusions : This results show that inhalation of Cyperus rotundus L. essential oil effects on relaxation and decreasing stress.