The idea of a prolonged global liquidity trap is connected with the notion of secular stagnation, i.e. the possibility of a prolonged situation of low inflation and low growth at the global level.
The secular stagnation hypothesis in this case refers to the demand-side version promoted by Larry Summers 8, where a trend of planned savings systematically higher than planned investment implies a situation of persistent lack of demand and a negative output gap, interest rate at the LB and low inflation or even deflation.