reserve X for Complex_Banach_Algebra,
  w,z,z1,z2 for Element of X,
  k,l,m,n,n1, n2 for Nat,
  seq,seq1,seq2,s,s9 for sequence of X,
  rseq for Real_Sequence;

theorem Th28:
  1 <= Sum(||.z.|| rExpSeq)
proof
  ||. Partial_Sums(z ExpSeq).0 .|| =||. (z ExpSeq).0 .|| by BHSP_4:def 1
    .=||. 1.X.|| by Th13
    .=1 by CLOPBAN3:38;
  hence thesis by Th27;
end;
