Boundary vs. interior conditions associated with weighted composition operators
Kei Izuchi; Yuko Izuchi; Shûichi Ohno
Open Mathematics (2014)
- Volume: 12, Issue: 5, page 761-777
- ISSN: 2391-5455
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] Bonet J., Lindström M., Wolf E., Differences of composition operators between weighted Banach spaces of holomorphic functions, J. Aust. Math. Soc., 2008, 84(1), 9–20 http://dx.doi.org/10.1017/S144678870800013X Zbl1145.47020
- [2] Choa J.S., Izuchi K.J., Ohno S., Composition operators on the space of bounded harmonic functions, Integral Equations Operator Theory, 2008, 61(2), 167–186 http://dx.doi.org/10.1007/s00020-008-1579-4 Zbl1155.47027
- [3] Contreras M.D., Díaz-Madrigal S., Compact-type operators defined on Hsui, In: Function Spaces, Edwardsville, May 19–23, 1998, Contemp. Math., 232, American Mathematical Society, Providence, 1999, 111–118 Zbl0936.46010
- [4] Cowen C.C., MacCluer B.D., Composition Operators on Spaces of Analytic Functions, Stud. Adv. Math., CRC Press, Boca Raton, 1995 Zbl0873.47017
- [5] Galindo P., Lindström M., Essential norm of operators on weighted Bergman spaces of infinite order, J. Operator Theory, 2010, 64(2), 387–399 Zbl1211.47064
- [6] Gamelin T.W., Uniform Algebras, Prentice-Hall, Englewood Cliffs, 1969 Zbl0213.40401
- [7] Garnett J.B., Bounded Analytic Functions, Pure Appl. Math., 96, Academic Press, New York-London, 1981
- [8] Hosokawa T., Izuchi K., Essential norms of differences of composition operators on H ∞, J. Math. Soc. Japan, 2005, 57(3), 669–690 http://dx.doi.org/10.2969/jmsj/1158241928 Zbl1100.47022
- [9] Hosokawa T., Izuchi K., Ohno S., Topological structure of the space of weighted composition operators on H 1, Integral Equations Operator Theory, 2005, 53(4), 509–526 http://dx.doi.org/10.1007/s00020-004-1337-1 Zbl1098.47025
- [10] Izuchi K.J., Izuchi Y., Ohno S., Weighted composition operators on the space of bounded harmonic functions, Integral Equations Operator Theory, 2011, 71(1), 91–111 http://dx.doi.org/10.1007/s00020-011-1886-z Zbl1241.47023
- [11] Izuchi K.J., Izuchi Y., Ohno S., Path connected components in weighted composition operators on h ∞ and H ∞ with the operator norm, Trans. Amer. Math. Soc., 2013, 365(7), 3593–3612 http://dx.doi.org/10.1090/S0002-9947-2012-05730-8 Zbl1282.47048
- [12] Izuchi K.J., Izuchi Y., Ohno S., Path connected components in weighted composition operators on h ∞ and H ∞ with the essential operator norm, Houston J. Math. (in press) Zbl1303.47045
- [13] Lindström M., Wolf E., Essential norm of the difference of weighted composition operators, Monatsh. Math., 2008, 153(2), 133–143 http://dx.doi.org/10.1007/s00605-007-0493-1 Zbl1146.47015
- [14] MacCluer B., Ohno S., Zhao R., Topological structure of the space of composition operators on H ∞, Integral Equations Operator Theory, 2001, 40(4), 481–494 http://dx.doi.org/10.1007/BF01198142 Zbl1062.47511
- [15] Moorhouse J., Compact differences of composition operators, J. Funct. Anal., 2005, 219(1), 70–92 http://dx.doi.org/10.1016/j.jfa.2004.01.012 Zbl1087.47032
- [16] Nieminen P.J., Saksman E., On compactness of the difference of composition operators, J. Math. Anal. Appl., 2004, 298(2), 501–522 http://dx.doi.org/10.1016/j.jmaa.2004.05.024 Zbl1072.47021
- [17] Rudin W., Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1987 Zbl0925.00005
- [18] Shapiro J.H., Composition Operators and Classical Function Theory, Universitext Tracts Math., Springer, New York, 1993 Zbl0791.30033
- [19] Shapiro J.H., Sundberg C., Isolation amongst the composition operators, Pacific J. Math., 1990, 145(1), 117–152 http://dx.doi.org/10.2140/pjm.1990.145.117 Zbl0732.30027