Relative boundedness and relative compactness for linear operators in Banach spaces

Binding, P.; Hryniv, R.

doi:10.1090/S0002-9939-00-05729-4

Relative boundedness and relative compactness for linear operators in Banach spaces
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Proc. Amer. Math. Soc. 128 (2000), 2287-2290 Request permission

Abstract:

If $A$ and $B$ are linear operators acting between Banach spaces, we show that compactness of $B$ relative to $A$ does not in general imply that $B$ has $A$-bound zero. We do, however, give conditions under which the above implication is valid.

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