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On the operator equation $ TX-XV=A$


Author: Constantin Apostol
Journal: Proc. Amer. Math. Soc. 59 (1976), 115-118
MSC: Primary 47A60; Secondary 47B47
DOI: https://doi.org/10.1090/S0002-9939-1976-0412856-3
MathSciNet review: 0412856
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Abstract: A characterization of the operators $ A$ for which the equation $ TX - XV = A$ is solvable is given, where $ T$ is a fixed right invertible operator and $ V$ is a fixed unilateral shift.


References [Enhancements On Off] (What's this?)

  • [1] C. Apostol, Commutators on Hilbert space, Rev. Roumaine Math. Pures Appl. 18 (1973), 1013-1024. MR 49 #1208. MR 0336434 (49:1208)
  • [2] N. Salinas, Reducing essential eigenvalues, Duke Math. J. 40 (1973), 561-580. MR 0390816 (52:11639)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0412856-3
Keywords: Operator equation, shift
Article copyright: © Copyright 1976 American Mathematical Society

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