Distortion of Banach spaces and supermultiplicative operational quantities

We prove that certain operational quantities q which characterize upper-semi Fredholm operators are supermultiplicative, in the sense of that q ( S ) q ( T ) ⩽ q ( S T ) . Based on the distortion of Banach spaces we show that another is not supermultiplicative. Moreover we introduce two supermultiplicative operational quantities which characterize also the upper-semi Fredholm operators and we prove that they are not equivalent to some operational quantities known.