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- W2071629905 abstract "Proof For each i, let Li be the lattice of subspaces of H generated by the ranges and the kernels of T k i , k = 0,1,2, . . . . Let us show that Li = Lj for all i and j . It is enough to establish that ranT k i = ranT k j and kerT k i = kerT k j , k = 0,1,2, . . . . If k = 0, the statement is trivial. Assume by induction that the statement is proved for some k. Pick x ∈ ranT k+1 i . There is y ∈ H such that x = T k+1 i y = TiT k i y. Since ranT k i = ranT k j , there is z ∈ H such that T k i y = T k j z. Then x = TiT k j z. By commutativity, x = T k j Tiz. Since ranTi = ranTj by the assumptions of the theorem, there is v ∈ H such that x = T k j Tj v = T k+1 j v. So, ranT k+1 i = ranT k+1 j . Similarly," @default.
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- W2071629905 date "2013-08-30" @default.
- W2071629905 modified "2023-09-24" @default.
- W2071629905 title "Erratum to: Semigroups of partial isometries" @default.
- W2071629905 doi "https://doi.org/10.1007/s00233-013-9526-3" @default.
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