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Essential norms of linear combinations of composition operators on h∞

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It is studied the linear combinations of composition operators on the Banach space of bounded harmonic functions on the open unit disk. We determine the essential norm of them.

Abstract

It is studied the linear combinations of composition operators on the Banach space of bounded harmonic functions on the open unit disk. We determine the essential norm of them.

참고문헌 (13)

  1. J. S. Choa, "Composition operators on the space of bounded harmonic functions", Integral Equations Operator Theory, 61(2), pp.167~186 (2008)
  2. C. C. Cowen, "Composition Operators on Spaces of Analytic Functions" (1995), CRC Press
  3. K. de Leeuw, "Extreme points and extremum problems in H1", Pacific J. Math, 8, pp.467~485 (1958)
  4. J. Garnett, "Bounded Analytic Functions" (1981), Academic Press
  5. P. Gorkin, "Norms and essential norms of linear combinations of endo- morphisms", Trans. Amer. Math. Soc, 358(2), pp.553~571 (2006)
  6. P. Gorkin, "Homotopic composition operators on H1(Bn), Function spaces", Contemp. Math., 328, pp.177~188 (2003), Amer. Math. Soc.
  7. K. Hoffman, "Banach Spaces of Analytic Functions" (1962), Prentice H
  8. T. Hosokawa, "Essential norms of differences of composition operators on H1", J. Math. Soc. Japan, 57(3), pp.669~690 (2005)
  9. T. Hosokawa, "Topological structure of the space of weighted composition operators on H1", Integral Equations Operator Theory, 53(4), pp.509~526 (2005)
  10. T. Hosokawa, "Isolated points and essential components of composition operators on H1", Proc. Amer. Math. Soc, 130(6), pp.1765~1773 (2002)
  11. K. J. Izuchi, "Linear combinations of composition operators on H1", J. Math. Anal. Appl, 338(2), pp.820~839 (2008)
  12. B. MacCluer, "Topological structure of the space of composition operators on H1", Integral Equations Operator Theory, 40(4), pp.481~494 (2001)
  13. J. Shapiro, "Composition Operators and Classical Function Theory" (1993), Springer-Verlag

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