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Banach-Mazur distance between Banach spaces of continuous functions
Havelka, Jonáš ; Cúth, Marek (advisor) ; Rondoš, Jakub (referee)
In this bachelor thesis, we examine estimates of a Banach-Mazur distance between spaces C(ω) and C(ω · k) for various k ∈ N. With a properly chosen form of mapping, we constructively show the best currently known upper bounds of this distance for all k. Besides the known bounds d(C(ω), C(ω · k)) ≤ 2 + √ 5 for any k > 3, and d(C(ω), C(ω · 2)) ≤ 3, we are going to find, for k = 3, the better bound, namely d(C(ω), C(ω · 3)) ≤ 4 instead of already known 2 + √ 5. 1
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