Abstract
We show that for every Banach space $X, \dim X>1$, every maximal commutative subalgebra of $L(X)$ has uncountably many copies between maximal commutative subalgebras of $L(X)$. Answering to a question of Aleksander Pe{\l}czy\'nski, we show also that for an arbitrary infinite dimensional Banach space $X$ there are at least countably many multiplications making of $X$ a commutative unital Banach algebra.
Citation
Wiesław Żelazko. "All maximal commutative subalgebras occur in $L(X)$ uncountably many times." Funct. Approx. Comment. Math. 53 (2) 189 - 192, December 2015. https://doi.org/10.7169/facm/2015.53.2.2
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