It shows that a compact operator K on an infinite - dimensional Banach space has spectrum that is either a finite subset of C which includes 0 .
The spectrum is a countably infinite subset of C which has 0 as its only limit point .
It shows that a compact operator K on an infinite - dimensional Banach space has spectrum that is either a finite subset of C which includes 0 , or the spectrum is a countably infinite subset of C which has 0 as its only limit point .