Topological structure of the space of composition operators onH ∞
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
Components and isolated points of the topological space of composition operators onH ∞ in the uniform operator topology are characterized. Compact differences of two composition operators are also characterized. With the aid of these results, we show that a component inC(H ∞ ) is not in general the set of all composition operators that differ from the given one by a compact operator.
- E. Berkson, Composition operators isolated in the uniform operator topology,Proc. Amer. Math. Soc. 81 (1981), 230–232.
- C. C. Cowen and B. D. MacCluer, “Composition Operators on Spaces of Analytic Functions,” CRC Press, Boca Raton, 1995.
- J. Garnett, “Bounded Analytic Functions,” Academic Press, New York, 1981.
- B. D. MacCluer, Components in the space of composition operators,Integral Equations Operator Theory 12 (1989), 725–738.
- K. Madigan, Composition operators into Lipschitz type spaces, Thesis, SUNY Albany,1993.
- J. H. Shapiro and C. Sundberg, Isolation amongst the composition operators,Pacific J. Math. 145 (1990), 117–152.
- K. Zhu, “Operator Theory in Function Spaces,” Marcel Dekker, New York, 1990.
- K. Zhu, Distances and Banach spaces of holomorphic functions on complex domains,J. London Math. Soc. (2)49 (1994), 163–182.
- Topological structure of the space of composition operators onH ∞
Integral Equations and Operator Theory
Volume 40, Issue 4 , pp 481-494
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links