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Similarity of a Triangular Operator to a Diagonal Operator

Abstract

We give sufficient conditions under which the non-self-adjoint operator A = G + iV 1/2 JV 1/2 (with a well-defined imaginary part) is similar to a self-adjoint one. We also give sufficient conditions (these conditions become necessary in the dissipative case) under which the triangular operator \(f \mapsto \alpha (x)f(x) + i\int_x^1 {k(x,t)f(t)d\mu (t)} \) is similar to a self-adjoint one. Bibliography: 34 titles.

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Malamud, M.M. Similarity of a Triangular Operator to a Diagonal Operator. Journal of Mathematical Sciences 115, 2199–2222 (2003). https://doi.org/10.1023/A:1022888921572

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Keywords

  • Imaginary Part
  • Diagonal Operator
  • Triangular Operator
  • Dissipative Case