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The hyperinvariant subspace lattice of a linear transformation. (English) Zbl 0359.47005


MSC:

47A15 Invariant subspaces of linear operators
15A21 Canonical forms, reductions, classification
Full Text: DOI

References:

[1] T. Andô and T. Sekiguchi, Hyperinvariant subspaces of a nilpotent operator, unpublished.; T. Andô and T. Sekiguchi, Hyperinvariant subspaces of a nilpotent operator, unpublished.
[2] Brickman, L.; Fillmore, P. A., The invariant subspace lattice of a linear transformation, Can. J. Math., 19, 810-822 (1967), MR 35, 4242. · Zbl 0153.04801
[3] John B. Conway and Pei Yuan Wu, the Splitting of \(AT_1T_2\); John B. Conway and Pei Yuan Wu, the Splitting of \(AT_1T_2\) · Zbl 0327.46075
[4] Donnellan, T., Lattice Theory (1968), Pergamon: Pergamon Oxford · Zbl 0194.32503
[5] Douglas, R. G.; Pearcy, Carl, On a topology for invariant subspaces, J. Funct. Anal., 2, 323-341 (1968), MR38, 1547. · Zbl 0174.17903
[6] Douglas, R. G.; Pearcy, Carl; Salinas, Norberto, Hyperinvariant subspaces via topological properties of lattices, Mich. Math. J., 20, 109-113 (1973) · Zbl 0268.47009
[7] Halmos, P. R., Eigenvectors and adjoints, Linear Algebra Appl., 4, 11-15 (1971) · Zbl 0264.15001
[8] Herrero, Domingo A.; Salinas, Norberto, Analytically invariant and bi-invariant subspaces, Trans. Amer. Math. Soc., 173, 117-136 (1972) · Zbl 0253.46126
[9] Hoffman, K.; Kunze, R., Linear Algebra (1971), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0212.36601
[10] W.E. Longstaff, A sufficient condition for hyperinvariance, preprint.; W.E. Longstaff, A sufficient condition for hyperinvariance, preprint. · Zbl 0371.47008
[11] Radjavi, Heydar; Rosenthal, P., Invariant Subspaces (1973), Springer: Springer New York · Zbl 0269.47003
[12] Rosenthal, P., A note on unicellular operators, Proc. Am. Math. Soc., 19, 505-506 (1968), MR36, 5753. · Zbl 0161.34503
[13] Stampfli, J. G., On hyponormal and Toeplitz operators, Math. Ann., 183, 328-336 (1969), MR 40, 4798. · Zbl 0175.43104
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