The lattices of invariant subspaces of a class of operators on the Hardy space
In the authors’ first paper, a Beurling-Rudin-Korenbljum type characterization of the closed ideals in a certain algebra of holomorphic functions was used to describe the lattice of invariant subspaces of the shift plus a complex Volterra operator. The current work is an extension of the previous work and it describes the lattice of invariant subspaces of the shift plus a positive integer multiple of the complex Volterra operator on the Hardy space. Our work was motivated by a paper by Ong who studied the real version of the same operator.
KeywordsComplex analysis Invariant subspaces Hardy space
Mathematics Subject Classification47A15
Unable to display preview. Download preview PDF.
- 2.A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 17 ppGoogle Scholar
- 5.B. I. Korenbljum, Invariant subspaces of the shift operator in a weighted Hilbert space, (Russian) Mat. Sb. (N.S.) 89 (131) (1972), 110-137Google Scholar
- 10.S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Edited and with a foreword by S.M. Nikol’ ski, Translated from the 1987 Russian original, Revised by the authors, Gordon and Breach Science Publishers, Yverdon, 1993.Google Scholar
- 12.D. Sarason, Invariant subspaces, In: Topics in Operator Theory, 1-47, Math. Surveys, No. 13, Amer. Math. Soc., Providence, RI, 1974.Google Scholar