Abstract
Abstract In this note we obtain some characterizations of Banach spaces which are not isomorphic to any of their proper subspaces. In particular, we show that a Banach space X is not isomorphic to any of its proper subspaces if and only the equality σRD(LT) = σLD(T) holds for every bounded linear operator T on X if and only if int(σ(T)) ⊆ σLD(T) holds for every bounded linear operator T on X, where LT denotes the left multiplication operator by T.
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