COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL

doi:10.1016/S0252-9602(11)60353-6

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1679-1693.doi: 10.1016/S0252-9602(11)60353-6

COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL

江良英|欧阳才衡

Department of Mathematics, Tongji University, Shanghai 200092, China；Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, China； Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China

收稿日期:2010-08-16 出版日期:2011-09-20 发布日期:2011-09-20
基金资助:
This work is part of the first author’s doctoral thesis (see [1]), but the proof of Theorem 3.1 is improved and some related results are obtained. Supported by the National Natural Science Foundation of China (10971219), and by Shanghai Education Research and Innovation Project (10YZ185) and Shanghai University Research Special Foundation for Outstanding Young Teachers (sjr09015).

COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL

JIANG Liang-Ying, OUYANG Cai-Heng

Department of Mathematics, Tongji University, Shanghai 200092, China；Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, China； Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China

Received:2010-08-16 Online:2011-09-20 Published:2011-09-20

摘要/Abstract

摘要：

We find a lower bound for the essential norm of the difference of two compo-sition operators acting on H²(B_N) or A²_s(B_N) (s > −1). This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.

关键词: composition operators, Hardy space, Bergman spaces, compact differences

Abstract:

Key words: composition operators, Hardy space, Bergman spaces, compact differences

中图分类号:

47B33

江良英, 欧阳才衡. COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL[J]. 数学物理学报(英文版), 2011, 31(5): 1679-1693.

JIANG Liang-Ying, OUYANG Cai-Heng. COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL[J]. Acta mathematica scientia,Series B, 2011, 31(5): 1679-1693.

参考文献

[1] Jiang L Y. Linear Fractional Composition Operators on Holomorphic Function Spaces [D]. Chinese Academy of Sciences, 2008 (in Chinese)

[2] Rudin W. Function Theory in the Unit Ball of CN. New York: Springer-Verlag, 1980

[3] Zhu K H. Spaces of Holomorphic Functions in the Unit Ball. New York: Springer-Verlag, 2005

[4] Shapiro J H. Composition Operators and Classical Function Theory. New York: Springer-Verlag, 1993

[5] Cowen C C, MacCluer B D. Composition Operators on Spaces of Analytic Functions. Boca Raton: CRC Press, 1995

[6] Berkson E. Composition operators isolated in the uniform operator topology. Proc Amer Math Soc, 1981, 81: 230–232

[7] Shapiro J H, Sundberg C. Isolation amongst the composition operators. Pacific J Math, 1990, 145: 117–152

[8] Heidler H. Algebraic and essentially algebraic composition operators on the ball or polydisk//Studies on Composition Operators (Laramie, 1996). Contemporary Math, 213. Amer Math Soc, 1998: 43–56

[9] Hammond C, MacCluer B D. Isolation and component structure in spaces of compoaition operators. Integr Equ Oper Theory, 2005, 53: 269–285

[10] MacCluer B D. Components in the space of composition operators. Integr Equ Oper Theory, 1989, 12: 725–738

[11] Gallardo-Guti´errez E A, Gonz´alez M J, Nieminen P J, Saksman E. On the connected component of compact composition operators on the Hardy space. Adv Math, 2008, 219: 986–1001

[12] Kriete T, Moorhouse J. Linear relations in the Calkin algebra for composition operators. Trans Amer Math Soc, 2007, 359: 2915-2944

[13] Shapiro J H. Aleksandrov measures used in essential norm inequalities for composition operators. J Oper Theory, 1998, 40: 133–146

[14] Bourdon P S. Components of linear fractional composition operators. J Math Anal Appl, 2003, 279: 228-245

[15] Moorhouse J. Compact differences of composition operators. J Funct Anal, 2005, 219: 70-92

[16] MacCluer B D, Weir R J. Linear-fractional composition operators in several variables. Integr Equ Oper Theory, 2005, 53: 373–402

[17] Jiang L Y, Ouyang C H. Essential normality of linear fractional composition operators in the unit ball of CN. Sci China Series A, 2009, 52: 2668–2678

[18] Cowen C C, MacCluer B D. Linear fractional maps of the unit ball and their composition operators. Acta Sci Math (Szeged), 2000, 66: 351–376

COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL

COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON HOLOMORPHIC FUNCTION SPACES IN THE UNIT BALL

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