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Research articles

ScienceAsia 44(2018): 340-345 |doi: 10.2306/scienceasia1513-1874.2018.44.340


On the Ptolemy constant of Lorentz sequence spaces and their duals


Zhan-fei Zuoa,b

 
ABSTRACT:     The Ptolemy constant of two-dimensional Lorentz sequence spaces is computed in this paper. On the way, we also calculate the Ptolemy constant in the dual space of two-dimensional Lorentz sequence spaces in the case of q = 1 and q ? 2. Moreover, we determine the Ptolemy constant of absolute normalized norms under some new conditions. These results which not only contain some previous results, but also give the exact value of the Ptolemy constant in some concrete Banach spaces.

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a Department of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404100 China.
b Key Laboratory of Intelligent Information Processing and Control, Chongqing Three Gorges University, Wanzhou, Chongqing 404100 China.

* Corresponding author, E-mail: zuozhanfei@163.com

Received 28 Dec 2017, Accepted 24 Jun 2018