A 0-2 law for cosine families with to ∞

الأصل · EN

For (C(t))t being a cosine family on a unital normed algebra, we show that the estimate ₜ→∞⁺C(t) - I <2 implies that C(t)=I for all t. This generalizes the result that ₜ≥₀C(t)-I<2 yields that C(t)=I for all t≥0. We also state the corresponding result for discrete cosine families and for semigroups.