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## Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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## A Banach space C(K) reading the dimension of K

Prelegent: Damian Głodkowski

2022-05-18 16:15

We show that if Jensen's diamond principle holds, then for every natural number n there is a compact space K, such that whenever L is compact space and the Banach spaces of continuous functions C(K) and C(L) are isomorphic, the covering dimension of L is equal to n. The constructed space K is a separable connected compact space with the property that every linear bounded operator T on C(K) is a weak multiplication i.e. it is of the form T=g*Id+S, where g is an element of C(K) and S is weakly compact.