Discrete Duhamel product, restriction of weighted shift operators and related problems

摘要

By applying the discrete Duhamel product method we calculate the spectralmultiplicity of the direct sum of some operators. In particular, we prove thatμ(T|Xi⊕ A)=1+μ(A) and μ(S⊕ A)=2 for the restriction of the weighted shift operator T|Xi,shift operator S and some appropriate operators A on the Banach spaces.