Abstract
If T, A are Hilbert space operators such that A is the norm-limit of operators similar to T, then there exists a continuous function γ from [0,1] into the algebra of operators such that γ(t) is a limit of similarities of T for all t in the interval [0,1], γ(0)=T and γ(1)=A.
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Apostol, C., Fialkow, L. A., Herrero, D. A., Voiculescu, D.: Approximation of Hilbert space operators. Vol. II, Research Notes in Math. 102, Pitman, Boston-London-Melbourne, 1984.
Gellar, R., Herrero, D. A.: Hyperinvariant subspaces of bilateral weighted shifts, Indiana Univ. Math. J. 23 (1974), 771–790.
Hadwin, D. W.: An operator-valued spectrum, Indiana Univ. Math. J. 26 (1977), 329–340.
Herrero, D. A.: Approximation of Hilbert space operators. Vol. I, Research Notes in Math. 72, Pitman, Boston-London-Melbourne, 1982.
Rosenblum, M.: On the operator equation BX−XA=Q, Duke Math. J. 23 (1956), 263–269.
Rota, G. C.: On models for linear operators, Comm. Pure Appl. Math. 13 (1960), 469–472.
Shields, A. L., Wallen, L.: The commutant of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971), 777–778.
Tong, A. E.: Diagonal nuclear operators in ℓp spaces, Trans. Amer. Math. Soc. 143 (1969), 235–247.
Tong, A. E.: Diagonal submatrices of matrix maps, Pac. J. Math. 32 (1970), 551–559.
Voiculescu, D.: A non-commutative Weyl-von Neumann theorem, Rev. Roum. Math. Pures et Appl. 21 (1976), 97–113.
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This research was partially supported by a Grant of the National Science Foundation.
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Herrero, D.A. The closure of a similarity orbit is always arcwise connected. Integr equ oper theory 10, 721–729 (1987). https://doi.org/10.1007/BF01195798
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DOI: https://doi.org/10.1007/BF01195798