Abstract
We show the existence of Banach spacesX,Ysuch that the set of strictly singular operatorsš®(X,Y)(resp., the set of strictly cosingular operatorsšš®(X,Y))would be strictly included inā±+(X,Y)(resp.,ā±ā(X,Y))for the nonempty class of closed densely defined upper semi-Fredholm operatorsĪ¦+(X,Y)(resp., for the nonempty class of closed densely defined lower semi-Fredholm operatorsĪ¦ā(X,Y)).
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