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About some convergence properties of sequences of \(B\)-valued cosine functions. (English) Zbl 1004.47028

Summary: Some convergence properties of sequences of \(B\)-valued cosine functions are established. It is shown that if a sequence of cosine functions is dominated and pointwise convergent, then the sequence of corresponding generators is convergent in the \(B\)-algebra. On the other hand, the convergence of the sequence of generators implies the convergence of the sequence of resolvent operators; from this last result, the convergence of the sequence of the corresponding cosine functions follows.

MSC:

47D09 Operator sine and cosine functions and higher-order Cauchy problems
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