The now canonical proof of Schwarz's Lemma appeared in a 1907 paper of Carathéodory, who attributed it to Erhard Schmidt. Since then, Schwarz's Lemma has acquired considerable fame, with multiple extensions and generalizations. Much less known is that, in the same year 1907, Landau and Toeplitz obtained a similar result where the diameter of the image set… (More)
In a previous paper the author proved that for square matrices with algebraic entries exp(A)exp(B) =exp(B)exp(A) if and only if AB = BA. This result is extended here to bounded operators on an arbitrary Banach space.
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