Geodesic
SUMS OF WEIGHTED COMPOSITION OPERATORS ON COP
Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 229-239

Voir la notice de l'article provenant de la source Cambridge University Press

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().
DOI : 10.1017/S0017089512000511
Mots-clés : Primary 47B38, 46J20, Secondary 30D55 
IZUCHI, KEI JI; IZUCHI, KOU HEI; IZUCHI, YUKO. SUMS OF WEIGHTED COMPOSITION OPERATORS ON COP. Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 229-239. doi: 10.1017/S0017089512000511
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[1] 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] 2.Cowen, C. and Maccluer, B., Composition operators on spaces of analytic functions (CRC Press, Boca Raton, FL, 1995). Google Scholar

[3] 3.Garnett, J., Bounded analytic functions (Academic Press, New York, 1981). Google Scholar

[4] 4.Gorkin, P., Decompositions of the maximal ideal space of L ∞, Trans. Am. Math. Soc. 282 (1984), 33–44. Google Scholar

[5] 5.Gorkin, P., Gleason parts and COP, J. Funct. Anal. 83 (1989), 44–49. Google Scholar | DOI

[6] 6.Hoffman, K., Bounded analytic functions and Gleason parts, Ann. Math. 86 (1967), 74–111. Google Scholar | DOI

[7] 7.Izuchi, K. and Ohno, S., Linear combinations of composition operators on H∞, J. Math. Anal. Appl. 378 (2008), 820–839. Google Scholar

[8] 8.Izuchi, K. and Ohno, S., Sums of weighted composition operators on H , J. Math. Anal. Appl. 384 (2011), 683–689. Google Scholar

[9] 9.Madigan, K. and Matheson, A., Compact composition operators on the Bloch space, Trans. Am. Math. Soc. 347 (1995), 2679–2687. Google Scholar

[10] 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] 11.Sarason, D., Algebras of functions on the unit circle, Bull. Am. Math. Soc. 79 (1973), 286–299. Google Scholar

[12] 12.Sarason, D., Functions of vanishing mean oscillation, Trans. Am. Math. Soc. 207 (1975), 391–405. Google Scholar | DOI

[13] 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] 14.Shapiro, J., Composition operators and classical function theory (Springer-Verlag, New York, 1993). Google Scholar | DOI

[15] 15.Smith, W., Compactness of composition operators on BMOA, Proc. Am. Math. Soc. 127 (1999), 2715–2725. Google Scholar

[16] 16.Sundberg, C. and Wolff, T., Interpolating sequences for QA, Trans. Am. Math. Soc. 276 (1983), 551–581. Google Scholar

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