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The compact operators are not complemented in $ \mathcal{B}(\mathcal{H})$


Author: John B. Conway
Journal: Proc. Amer. Math. Soc. 32 (1972), 549-550
MSC: Primary 46.10; Secondary 47.00
DOI: https://doi.org/10.1090/S0002-9939-1972-0288559-1
MathSciNet review: 0288559
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Abstract: If $ \mathcal{H}$ is an infinite dimensional Hilbert space then it is shown that the space of compact operators is not complemented in the space of all bounded operators.


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

  • [1] E. O. Thorp, Projections onto the subspace of compact operators, Pacific J. Math. 10 (1960), 693-696. MR 22 #4955. MR 0114128 (22:4955)
  • [2] D. Arterburn and R. Whitley, Projections in the space of bounded linear operators, Pacific J. Math. 15 (1965), 739-746. MR 32 #4507. MR 0187052 (32:4507)
  • [3] R. Whitley, Projecting m onto $ {c_0}$, Amer. Math. Monthly 73 (1966), 285-286. MR 1533692

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288559-1
Keywords: Hilbert space, bounded operators, compact operators, noncomplemented subspace
Article copyright: © Copyright 1972 American Mathematical Society

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