• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.249-259
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• 2022

Let 𝓐 be a unital C^*-algebra. Then it follows that $\sum\limits_{i=1}^{n}(a_ia^*_i)^{\frac{1}{2}}{\leq}\sqrt{n}\(\sum\limits_{i=1}^{n}a_ia^*_i\)^{\frac{1}{2}}$, ∀n ∈ ℕ, ∀a₁, …, a_n ∈ 𝓐. By modifications of arguments of Botelho-Andrade, Casazza, Cheng, and Tran given in 2019, for certain n-tuple x = (a₁, …, a_n) ∈ 𝓐ⁿ, we give a method to compute a positive element c_x in the C^*-algebra 𝓐 such that the equality $$\sum\limits_{i=1}^{n}(a_ia^*_i)^{\frac{1}{2}}=c_x\sqrt{n}\(\sum\limits_{i=1}^{n}a_ia^*_i\)^{\frac{1}{2}}$$ holds. We give an application for the integral of Kasparov. We also derive a formula for the exact constant for the continuous ℓ₁ - ℓ₂ inequality.

• The Journal of the Korea Contents Association
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• v.14 no.9
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• pp.267-274
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• 2014

The culture is an integral factor when we deal with the quality of life of members of society, and the cultural right is accepted as the basic right. However, the cultural right of the disabled in our society stays in the conditions of the discrimination and alienation by social prejudices and barriers against people with disabilities, and that results from the lack of understanding as a right. The aim of this study is to further raise awareness about the cultural right of the disabled as the basic human right, make it clear to be a universal right based on that, and insist on implementing 'Affirmative Action' for actualizing the disabled's cultural right to equality. The political measures derived from this study to guarantee and realize the cultural right of the disabled are as follows. First, the target extent of cultural voucher system should be expand to not recipients of national basic livelihood guarantees and near poverty groups, but all the disabled. Second, to take full charge of the cultural support of the disabled as a independent organization, it is necessary to establish Ministry of Culture, Sports and Tourism-affiliated 'Bureau of Culture for Persons with Disabilities'. Third, the nationwide survey on cultural activities and desires of the disabled periodically is required.