Invariant subspaces for the family of operators which commute with a completely continuous operator

@article{Lomonosov1973InvariantSF,
  title={Invariant subspaces for the family of operators which commute with a completely continuous operator},
  author={Victor I. Lomonosov},
  journal={Functional Analysis and Its Applications},
  year={1973},
  volume={7},
  pages={213-214}
}
  • V. Lomonosov
  • Published 1973
  • Mathematics
  • Functional Analysis and Its Applications
View on Springer
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References

SHOWING 1-3 OF 3 REFERENCES
Ten problems in Hilbert space
Solution of an invariant subspace problem of K
An electronic regulating arrangement in which an analog signal generator is either inductively or capacitatively coupled with an electrically conductive element having an edge displaceable with… Expand
INVARIANT SUBSPACES OF COMPLETELY CONTINOUS OPERATIONS
Abstract : A proof is presented of the theorem that if B is a Banach space and if T is a completely continuous operator in B, there then exist proper invariant subspaces of T. The proof assumes… Expand