L does not equal 1.

L is the lag operator with specific properties.

Example:

c:constant,  L*c=c

Yt: time series , L*Yt=Yt-1 etc (see any time series textbook for these)

Regarding your question since c(2) is a constant we write c(2)*L=c(2).

This applies to polynomials as well. If A(L)=1-a1*L-a2*L^2 then A(L)*c=…=A(1)*c

Now if in the denominator c/(1-a*L)=c/(1-a).

Further, if |a|<1 then c/(1-a)=c*sum(a^j) for j=0 to infinity (series property).  Thus c/(1-a)= c*sum(a^j)=c*sum((aL)^j)=c*sum(a^j*L^j)

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Dr Ioannis A. Venetis

Assistant Professor

University of Patras, Department of Economic Sciences

University Campus, Rio, 26504, Greece

Tel: +30 2610 969 964

Ιωάννης Α. Βενέτης

Επίκουρος Καθηγητής

Τμήμα Οικονομικών Επιστημών, Πανεπιστήμιο Πατρών

Πανεπιστημιούπολη, Ρίο 26504

Τηλ: 2610 969 964

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