A characterization of the invariant subspaces of direct sums of strictly cyclic algebras

Rosenthal, Erik

doi:10.1090/S0002-9939-1985-0792273-2

A characterization of the invariant subspaces of direct sums of strictly cyclic algebras
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Proc. Amer. Math. Soc. 94 (1985), 624-628 Request permission

Abstract:

Two characterizations of the invariant subspace lattice of ${A^{(n)}}$ for a strictly cyclic operator algebra $A$ on a separable Hilbert space are proven.

References

William B. Arveson, A density theorem for operator algebras, Duke Math. J. 34 (1967), 635–647. MR 221293
W. F. Donoghue Jr., The lattice of invariant subspaces of a completely continuous quasi-nilpotent transformation, Pacific J. Math. 7 (1957), 1031–1035. MR 92124
Mary R. Embry, Maximal invariant subspaces of strictly cyclic operator algebras, Pacific J. Math. 49 (1973), 45–50. MR 336386
Ciprian Foiaş and J. P. Williams, Some remarks on the Volterra operator, Proc. Amer. Math. Soc. 31 (1972), 177–184. MR 295126, DOI 10.1090/S0002-9939-1972-0295126-2
Paul R. Halmos, Finite-dimensional vector spaces, The University Series in Undergraduate Mathematics, D. Van Nostrand Co., Inc., Princeton-Toronto-New York-London, 1958. 2nd ed. MR 0089819
James H. Hedlund, Strongly strictly cyclic weighted shifts, Proc. Amer. Math. Soc. 57 (1976), no. 1, 119–121. MR 402530, DOI 10.1090/S0002-9939-1976-0402530-1
Domingo A. Herrero, Transitive algebras of operators that contain a subalgebra of finite strict multiplicity, Rev. Un. Mat. Argentina 26 (1972/73), 77–84 (Spanish). MR 336387
Domingo A. Herrero, Operator algebras of finite strict multiplicity, Indiana Univ. Math. J. 22 (1972/73), 13–24. MR 315468, DOI 10.1512/iumj.1972.22.22003
Domingo A. Herrero and Alan Lambert, On strictly cyclic algebras, ${\scr P}$-algebras and reflexive operators, Trans. Amer. Math. Soc. 185 (1973), 229–235. MR 328619, DOI 10.1090/S0002-9947-1973-0328619-5
Edward Kerlin and Alan Lambert, Strictly cyclic shifts on $l_{p}$, Acta Sci. Math. (Szeged) 35 (1973), 87–94. MR 328658

Strictly cyclic operator algebras

Alan Lambert, Strictly cyclic weighted shifts, Proc. Amer. Math. Soc. 29 (1971), 331–336. MR 275213, DOI 10.1090/S0002-9939-1971-0275213-4
Alan Lambert, Strictly cyclic operator algebras, Pacific J. Math. 39 (1971), 717–726. MR 310664
A. L. Lambert and T. R. Turner, The double commutant of invertibly weighted shifts, Duke Math. J. 39 (1972), 385–389. MR 310683
N. K. Nikol′skiĭ, Invariant subspaces of weighted shift operators, Mat. Sb. (N.S.) 74 (116) (1967), 172–190 (Russian). MR 0229081
Eric A. Nordgren, Closed operators commuting with a weighted shift, Proc. Amer. Math. Soc. 24 (1970), 424–428. MR 257786, DOI 10.1090/S0002-9939-1970-0257786-X
Eric A. Nordgren, Invariant subspaces of a direct sum of weighted shifts, Pacific J. Math. 27 (1968), 587–598. MR 240657
Heydar Radjavi and Peter Rosenthal, Invariant subspaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 77, Springer-Verlag, New York-Heidelberg, 1973. MR 0367682
Erik J. Rosenthal, Power bounded strictly cyclic operators, Proc. Amer. Math. Soc. 72 (1978), no. 2, 276–280. MR 507322, DOI 10.1090/S0002-9939-1978-0507322-2
Erik J. Rosenthal, A Jordan form for certain infinite-dimensional operators, Acta Sci. Math. (Szeged) 41 (1979), no. 3-4, 365–374. MR 555430
Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974, pp. 49–128. MR 0361899