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On two questions of Halmos concerning subspace lattices


Authors: W. E. Longstaff and Peter Rosenthal
Journal: Proc. Amer. Math. Soc. 75 (1979), 85-86
MSC: Primary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1979-0529219-5
MathSciNet review: 529219
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Abstract: An example is constructed of a nonreflexive pentagonal lattice of subspaces. It follows that reflexivity is not invariant under lattice isomorphism, even for finite lattices.


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

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  • [2] P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887-933. MR 0270173 (42:5066)
  • [3] -, Reflexive lattices of subspaces, J. London Math. Soc. 4 (1971), 257-263. MR 0288612 (44:5808)
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  • [6] E. Nordgren, M. Radjabalipour, H. Radjavi and P. Rosenthal, On invariant operator ranges, Trans. Amer. Math. Soc. (to appear). MR 531986 (81c:47010)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0529219-5
Keywords: Reflexive lattice, invariant subspace
Article copyright: © Copyright 1979 American Mathematical Society

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