We show that any convolution operator induced by a non-constant polynomial that vanishes at zero supports a hypercyclic algebra. This partially solves a question raised by R. Aron.

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We show that the set ℓ ∞ ∖ c 0 \ell ^{\infty }\setminus c_0 is maximal dense-lineable and densely strongly c \mathfrak {c} -algebrable answering a question posed by Nestoridis and complementing a result by García-Pacheco, Martín and Seoane-Sepúlveda.