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2014 | 12 | 5 | 761-777
Tytuł artykułu

Boundary vs. interior conditions associated with weighted composition operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Associated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk $$\mathbb{D}$$, we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior $$\mathbb{D}$$ and on the boundary $$\partial \mathbb{D}$$ respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
5
Strony
761-777
Opis fizyczny
Daty
wydano
2014-05-01
online
2014-02-15
Twórcy
autor
autor
Bibliografia
  • [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
  • [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
  • [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
  • [4] Cowen C.C., MacCluer B.D., Composition Operators on Spaces of Analytic Functions, Stud. Adv. Math., CRC Press, Boca Raton, 1995
  • [5] Galindo P., Lindström M., Essential norm of operators on weighted Bergman spaces of infinite order, J. Operator Theory, 2010, 64(2), 387–399
  • [6] Gamelin T.W., Uniform Algebras, Prentice-Hall, Englewood Cliffs, 1969
  • [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
  • [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
  • [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
  • [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
  • [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)
  • [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
  • [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
  • [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
  • [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
  • [17] Rudin W., Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1987
  • [18] Shapiro J.H., Composition Operators and Classical Function Theory, Universitext Tracts Math., Springer, New York, 1993
  • [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
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0377-7
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