>**Problem.** Is the separability of a semi-simple commutative Banach algebra $A$ equivalent to the existence of a countable family $\{\varphi_n\}_{n\in\omega}$ of multiplicative linear functionals on $A$ such that for each $a\in A$ its spectrum coincides with the closure of the union $\bigcup_{n\in\omega}\varphi_n(a)$?

(The problem was posed 09.08.2015 by Michal Wojciechowski on page 14 of [zeroth volume][1] of [Lviv Scottish Book][2]).

The prize for solution: *A dinner in "Szkocka"*. 


  [1]: http://www.math.lviv.ua/szkocka/viewbook.php?vol=0
  [2]: http://www.math.lviv.ua/szkocka