A new constant in Banach spaces based on the Zb$ \check{a} $ganu constant $ C_{Z}(B) $
In Banach spaces, first we present a new geometric constant, $ C_{Z}^{(q)}(t, B) $, which is closely related to the Zb$ \check{a} $ganu constant. We prove that $ \frac{(t+2)^{q}}{2^{q-1}\left(2^{q-1}+t^{q}\right)} $ and $ \frac{4}{3} $ are respectively the lower and upper bounds for $ C_{Z}^{(q)}(t,...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025296 |
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| Summary: | In Banach spaces, first we present a new geometric constant, $ C_{Z}^{(q)}(t, B) $, which is closely related to the Zb$ \check{a} $ganu constant. We prove that $ \frac{(t+2)^{q}}{2^{q-1}\left(2^{q-1}+t^{q}\right)} $ and $ \frac{4}{3} $ are respectively the lower and upper bounds for $ C_{Z}^{(q)}(t, B) $. Furthermore, we also derive that $ C_{Z}^{(q)}(t, B) = C_{Z}^{(q)}(t, \widetilde{B}) $, where $ \widetilde{B} $ denotes the ultrapower spaces of $ B $. Then, we can establish certain sufficient conditions that ensure a Banach spaces possesses a normal structure, which involve different constants such as the Zb$ \check{a} $ganu constant and Domínguez–Benavides coefficient. |
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| ISSN: | 2473-6988 |