Taiwanese Journal of Mathematics

TOPOLOGICAL STRUCTURE OF THE SPACE OF COMPOSITION OPERATORS FORM $F(p,q,s)$ SPACE to $\mathcal{B}_\mu$ SPACE

Li Zhang and Ze-Hua Zhou

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Abstract

We study the topological structure of the space of all bounded composition operators from $F(p,q,s)$ to $\mathcal{B}_\mu$ on the unit disk $\mathbb{D}$ in the operator norm topology. At the same time, we characterizes the boundedness and compactness of the differences of two composition operators.

Article information

Source
Taiwanese J. Math., Volume 18, Number 1 (2014), 285-304.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706344

Digital Object Identifier
doi:10.11650/tjm.18.2014.3398

Mathematical Reviews number (MathSciNet)
MR3162126

Zentralblatt MATH identifier
1357.32006

Subjects
Primary: 47B38: Operators on function spaces (general)
Secondary: 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions 47G10: Integral operators [See also 45P05] 47B33: Composition operators

Keywords
differences topological structure composition operators $F(p,q,s)$ space $\mathcal{B}_\mu$ space

Citation

Zhang, Li; Zhou, Ze-Hua. TOPOLOGICAL STRUCTURE OF THE SPACE OF COMPOSITION OPERATORS FORM $F(p,q,s)$ SPACE to $\mathcal{B}_\mu$ SPACE. Taiwanese J. Math. 18 (2014), no. 1, 285--304. doi:10.11650/tjm.18.2014.3398. https://projecteuclid.org/euclid.twjm/1499706344


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References

  • J. Bonet, M. Lindström and E. Wolf, Differences of composition operators between weighted Banach spaces of holomorphic functions, J. Austral. Math. Soc., 84(1) (2008), 9-20.
  • J. Bonet, M. Lindstr$\ddot{o}$m and E. Wolf, Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order, Integr. Equ. Oper. Theory, 65 (2009), 195-210.
  • C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, 1995.
  • T. Hosokawa, K. Izuchi and S. Ohno, Topological structure of the space of weighted composition operators on $H^\infty$, Integr. Equ. Oper. Theory, 53 (2005), 509-526.
  • T. Hosokawa, K. Izuchi and D. Zheng, Isolated points and essential components of composition operators on $H^\infty$, Proc. Amer. Math. Soc., 130(6) (2001), 1765-1773.
  • T. Hosokawa and S. Ohno, Topological structures of the sets of composition operatora on the Bloch spaces, J. Math. Anal. Appl., 314 (2006), 736-748.
  • T. Hosokawa and S. Ohno, Differences of composition operators on the Bloch spaces, J. Operator Theory, 57(2) (2007), 229-242.
  • K. Kellay and P. Lefèvre, Compact composition operators on weighted Hilbert spaces of analytic functions, J. Math. Anal. Appl., 386 (2012), 718-727.
  • M. Lindstöm and E. Wolf, Essential norm of the difference of weighted composition operators, Monatsh. Math., 153 (2008), 133-143.
  • J. Moorhouse, Compact differences of composition operators, J. Funct. Anal., 219 (2005), 70-92.
  • B. D. MacCluer, S. Ohno and R. Zhao, Topological structure of the space of composition operators on $H^\infty$, Integr. Equ. Oper. Theory, 40 (2001), 481-494.
  • S. Ohno, K. Stroethoff and R. Zhao, Weighted composition operators between Bloch-type spaces, Rocky Mountain J. Math., 33(1) (2003), 191-215.
  • E. Saukko, Difference of composition operators between standard weighted Bergman spaces, J. Math. Anal. Appl., 381 (2011), 789-798.
  • J. H. Shapiro, Composition Operators and Classical Function Theory, Spriger-Verlag, 1993.
  • A. K. Sharma and S. Ueki, Composition operators from Nevanlinna type spaces to Bloch type spaces, Banach J. Math. Anal., 6(1) (2012), 112-123.
  • W. F. Yang, Composition operators from $F(p,q,s)$ spaces to the $n$th weighted-type spaces on the unit disc, Appl. Math. Comput., 218 (2011), 1443-1448.
  • X. J. Zhang, The multipliers on several holomorphic function theory (in Chinese), Chinese Ann. Math. Ser A, 26(4) (2005), 477-486.
  • Z. H. Zhou and R. Y. Chen, Weighted composition operators fom $F(p, q, s)$ to Bloch type spaces on the unit ball, Internat. J. Math., 19(8) (2008), 899-926.
  • Z. H. Zhou and J. H. Shi, Compactness of composition operators on the Bloch space in classical bounded symmetric domains, Michigan Math. J., 50 (2002), 381-405.
  • K. H. Zhu, Operator Theory in Function Spaces, Marcel Dekker. Inc, New York, 1990.
  • K. H. Zhu, Bloch type spaces of analytic functions, Rocky Mountain J. Math., 23 (1993), 1143-1177.
  • K. H. Zhu, Spaces of Holomorphic Functions in the Unit Ball. Grad. Texts in Math., Springer, 2005.