Small transitive lattices
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- by D. W. Hadwin, W. E. Longstaff and Peter Rosenthal PDF
- Proc. Amer. Math. Soc. 87 (1983), 121-124 Request permission
Abstract:
Partial results are obtained on the problem of determining the smallest lattice of subspaces of a Hilbert space with the property that the only operators leaving all the subspaces invariant are the multiples of the identity.References
- P. A. Fillmore and J. P. Williams, On operator ranges, Advances in Math. 7 (1971), 254–281. MR 293441, DOI 10.1016/S0001-8708(71)80006-3
- Ciprian Foiaş, Invariant para-closed subspaces, Indiana Univ. Math. J. 21 (1971/72), 887–906. MR 293439, DOI 10.1512/iumj.1972.21.21072
- P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887–933. MR 270173, DOI 10.1090/S0002-9904-1970-12502-2
- K. J. Harrison, Heydar Radjavi, and Peter Rosenthal, A transitive medial subspace lattice, Proc. Amer. Math. Soc. 28 (1971), 119–121. MR 283609, DOI 10.1090/S0002-9939-1971-0283609-X
- E. Nordgren, M. Radjabalipour, H. Radjavi, and P. Rosenthal, On invariant operator ranges, Trans. Amer. Math. Soc. 251 (1979), 389–398. MR 531986, DOI 10.1090/S0002-9947-1979-0531986-6
- Sing Cheong Ong, Invariant operator ranges of nest algebras, J. Operator Theory 3 (1980), no. 2, 195–201. MR 578939
- Heydar Radjavi and Peter Rosenthal, Invariant subspaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 77, Springer-Verlag, New York-Heidelberg, 1973. MR 0367682
- Allen L. Shields, A note on invariant subspaces, Michigan Math. J. 17 (1970), 231–233. MR 440389
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 121-124
- MSC: Primary 47A15; Secondary 47D25
- DOI: https://doi.org/10.1090/S0002-9939-1983-0677246-0
- MathSciNet review: 677246