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SUMS OF WEIGHTED COMPOSITION OPERATORS ON COP

Published online by Cambridge University Press:  02 August 2012

KEI JI IZUCHI ,
KOU HEI IZUCHI  and
YUKO IZUCHI
KEI JI IZUCHI
Affiliation:
Department of Mathematics, Niigata University, Niigata 950-2181, Japan e-mail: izuchi@m.sc.niigata-u.ac.jp
KOU HEI IZUCHI
Affiliation:
Department of Mathematics, Faculty of Education, Yamaguchi University, Yamaguchi 753-8511, Japan e-mail: izuchi@yamaguchi-u.ac.jp
YUKO IZUCHI
Affiliation:
Aoyama-Shinmachi 18-6-301, Nishi-ku, Niigata 950-2006, Japan e-mail: yfd10198@nifty.com
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Abstract

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Let COP = 0 ∩ H∞, where 0 is the little Bloch space on the open unit disk , and A() be the disk algebra on . For non-zero functions u1,u2,. . ., uN ∈ A() and distinct analytic self-maps ϕ1,ϕ2,. . .,ϕN satisfying ϕj ∈ A() and ∥ϕj∥∞=1 for every j, it is given characterisations of which the sum of weighted composition operators ∑Nj=1ujCϕj maps COP into A().

Keywords

Primary 47B3846J20Secondary 30D55
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 1 , January 2013 , pp. 229 - 239
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

1.Chandra, H. and Singh, B., Compactness and norm of the sum of weighted composition operators on A(), Int. J. Math. Anal. (Ruse) 4 (2010), 1945–1956.Google Scholar
2.Cowen, C. and MacCluer, B., Composition operators on spaces of analytic functions (CRC Press, Boca Raton, FL, 1995).Google Scholar
3.Garnett, J., Bounded analytic functions (Academic Press, New York, 1981).Google Scholar
4.Gorkin, P., Decompositions of the maximal ideal space of L ∞, Trans. Am. Math. Soc. 282 (1984), 33–44.Google Scholar
5.Gorkin, P., Gleason parts and COP, J. Funct. Anal. 83 (1989), 44–49.CrossRefGoogle Scholar
6.Hoffman, K., Bounded analytic functions and Gleason parts, Ann. Math. 86 (1967), 74–111.CrossRefGoogle Scholar
7.Izuchi, K. and Ohno, S., Linear combinations of composition operators on H∞, J. Math. Anal. Appl. 378 (2008), 820–839.Google Scholar
8.Izuchi, K. and Ohno, S., Sums of weighted composition operators on H ∞, J. Math. Anal. Appl. 384 (2011), 683–689.Google Scholar
9.Madigan, K. and Matheson, A., Compact composition operators on the Bloch space, Trans. Am. Math. Soc. 347 (1995), 2679–2687.Google Scholar
10.Ohno, S., Differences of weighted composition operators on the disk algebra, Bull. Belg. Math. Soc. Simon Stevin 17 (2010), 101–107.Google Scholar
11.Sarason, D., Algebras of functions on the unit circle, Bull. Am. Math. Soc. 79 (1973), 286–299.Google Scholar
12.Sarason, D., Functions of vanishing mean oscillation, Trans. Am. Math. Soc. 207 (1975), 391–405.CrossRefGoogle Scholar
13.Sarason, D., The Shilov and Bishop decompositions of H ∞ + C, in Conference on harmonic analysis in honor of Antoni Zygmund, Chicago, IL, 1981, vols. I, II (Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983), 461–474.Google Scholar
14.Shapiro, J., Composition operators and classical function theory (Springer-Verlag, New York, 1993).CrossRefGoogle Scholar
15.Smith, W., Compactness of composition operators on BMOA, Proc. Am. Math. Soc. 127 (1999), 2715–2725.Google Scholar
16.Sundberg, C. and Wolff, T., Interpolating sequences for QAB, Trans. Am. Math. Soc. 276 (1983), 551–581.Google Scholar