I am trying to answer a question about a finite difference scheme. I need to show that the method is stable in the L1-norm. I can't find a single definition of what that means, so does anyone have a source or know for a fact what the definition is?

I'm guessing that if we denote the operator corresponding to the scheme as $H$, then we need to show that $$||H^n||_1 \le C$$ where $C>0$ is a constant.

Thanks.