Babescu, Gh. About some convergence properties of sequences of \(B\)-valued cosine functions. (English) Zbl 1004.47028 An. Univ. Timiș., Ser. Mat.-Inform. 35, No. 2, 151-160 (1997). 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 Keywords:linear bounded operator; spectral property; sequences of \(B\)-valued cosine functions; \(B\)-algebra; resolvent operators PDFBibTeX XMLCite \textit{Gh. Babescu}, An. Univ. Timiș., Ser. Mat.-Inform. 35, No. 2, 151--160 (1997; Zbl 1004.47028)