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Path Connected Components in the Spaces of Weighted Composition Operators with the Strong Operator Topology II


Affiliations
1 Department of Mathematics, Niigata University, Niigata 950-2181, Japan
2 Asahidori 2-2-23, Yamaguchi 753-0051, Japan
     

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The path connected components are determined in the space of weighted composition operators on the space of bounded harmonic functions with the strong operator topology.

Keywords

Weighted Composition Operator, Space of Bounded Harmonic Functions, Strong Operator Topology, Path Connected Component.
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  • R. Aron, P. Galindo and M. Lindstr¨om, Connected components in the space of composition operators in H∞ functions of many variables, Integral Equations Operator Theory 45(2003), 1–14.
  • J. Choa, K. J. Izuchi and S. Ohno, Composition operators on the space of bounded harmonic functions, Integral Equations Operator Theory 61(2008), 167–186.
  • C. C. Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995.
  • E. Gallardo-Guti´errez, M. Gonz´alez, P. Nieminen and E. Saksman, On the connected component of compact composition operators on the Hardy space, Adv. Math. 219(2008), 986–1001.
  • K. Hoffman, Banach Spaces of Analytic Functions, Prentice Hall, New Jersey, 1962.
  • T. Hosokawa and K. J. Izuchi, Essential norms of differences of composition operators on H∞, J. Math. Soc. Japan 57(2005), 669–690.
  • T. Hosokawa, K. J. Izuchi and S. Ohno, Topological structure of the space of weighted composition operators on H∞, Integral Equations Operator Theory 53(2005), 509–526.
  • T. Hosokawa, K. J. Izuchi and D. Zheng, Isolated points and essential components of composition operators on H∞, Proc. Amer. Math. Soc. 130(2002), 1765–1773.
  • K. J. Izuchi and Y. Izuchi, Path connected components in the spaces of weighted composition operators with the strong operator topology I, Inter. J. Funct. Anal. Op. Theory Appl. 7(2015), 161–176.
  • K. J. Izuchi, Y. Izuchi and S. Ohno, Weighted composition operators on the space of bounded harmonic functions, Integral Equations Operator Theory 71(2011), 91–111.
  • K. J. Izuchi, Y. Izuchi and S. Ohno, Path connected components in weighted composition operators on h∞ and H∞ with the operator norm, Trans. Amer. Math. Soc. 365(2013), 3593–3612.
  • B. MacCluer, Components in the space of composition operators, Integral Equations Operator Theory 12(1989), 725–738.
  • B. MacCluer, S. Ohno and R. Zhao, Topological structure of the space of composition operators on H∞, Integral Equations Operator Theory 40(2001), 481–494.
  • J. Manhas, Topological structures of the spaces of composition operators on spaces of analytic functions, Contemp. Math. 435(2007), 283–299.
  • W. Rudin, Real and Complex Analysis, Third Edition, McGraw-Hill, New York, 1987.
  • J. Ryff, Subordinate Hp functions, Duke Math. J. 33(1966), 347–354.
  • J. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993.
  • J. Shapiro and C. Sundberg, Isolation amongst the composition operators, Pacific J. Math. 145(1990), 117–152.

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  • Path Connected Components in the Spaces of Weighted Composition Operators with the Strong Operator Topology II

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Authors

Kei Ji Izuchi
Department of Mathematics, Niigata University, Niigata 950-2181, Japan
Yuko Izuchi
Asahidori 2-2-23, Yamaguchi 753-0051, Japan

Abstract


The path connected components are determined in the space of weighted composition operators on the space of bounded harmonic functions with the strong operator topology.

Keywords


Weighted Composition Operator, Space of Bounded Harmonic Functions, Strong Operator Topology, Path Connected Component.

References