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1998 | 127 | 3 | 201-222
Tytuł artykułu

Harmonic extensions and the Böttcher-Silbermann conjecture

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present counterexamples to a conjecture of Böttcher and Silbermann on the asymptotic multiplicity of the Poisson kernel of the space $L^∞(∂D)$ and discuss conditions under which the Poisson kernel is asymptotically multiplicative.
Słowa kluczowe
Czasopismo
Rocznik
Tom
127
Numer
3
Strony
201-222
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-05-20
poprawiono
1997-05-15
Twórcy
autor
  • Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837, U.S.A., pgorkin@bucknell.edu
autor
Bibliografia
  • [1] S. Axler, S.-Y. A. Chang and D. Sarason, Products of Toeplitz operators, Integral Equations Operator Theory 1 (1978), 285-309.
  • [2] S. Axler and Ž. Čučković, Commuting Toeplitz operators with harmonic symbols, ibid. 14 (1991), 1-12.
  • [3] S. Axler and P. Gorkin, Divisibility in Douglas algebras, Michigan Math. J. 31 (1984), 89-94.
  • [4] S. Axler and P. Gorkin, Algebras on the disk and doubly commuting multiplication operators, Trans. Amer. Math. Soc. 309 (1988), 711-723.
  • [5] S. Axler and D. Zheng, The Berezin transform on the Toeplitz algebra, Studia Math. 127 (1998), 113-136.
  • [6] A. Böttcher and B. Silbermann, Analysis of Toeplitz Operators, Akademie-Verlag, 1989, and Springer, 1990.
  • [7] A. Böttcher and B. Silbermann, Axler-Chang-Sarason-Volberg Theorems for harmonic approximation and stable convergence, in: Linear and Complex Analysis Problem Book 3, Part I, V. P. Havin and N. K. Nikol'skiĭ (eds.), Lecture Notes in Math. 1573, Springer, 1994, 340-341.
  • [8] P. Budde, Support sets and Gleason parts of $M(H^∞)$, thesis, Univ. of California, Berkeley, 1982.
  • [9] S.-Y. A. Chang, A characterization of Douglas subalgebras, Acta Math. 137 (1976), 81-89.
  • [10] R. G. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972.
  • [11] R. G. Douglas, Banach Algebra Techniques in the Theory of Toeplitz Operators, Regional Conf. Ser. in Math. 15, Amer. Math. Soc., 1972.
  • [12] T. W. Gamelin, Uniform Algebras, 2nd ed., Chelsea, 1984.
  • [13] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
  • [14] P. Gorkin, Decompositions of the maximal ideal space of $L^∞$, doctoral dissertation, Michigan State Univ., 1982.
  • [15] P. Gorkin, Hankel type operators, Bourgain algebras, and uniform algebras, preprint.
  • [16] P. Gorkin and K. Izuchi, Some counterexamples in subalgebras of $L^∞$, Indiana Univ. Math. J. 40 (1991), 1301-1313.
  • [17] P. Gorkin and R. Mortini, Interpolating Blaschke products and factorization in Douglas algebras, Michigan Math. J. 38 (1991), 147-160.
  • [18] P. Gorkin and D. Zheng, Essentially commuting Toeplitz operators, preprint.
  • [19] C. Guillory and K. Izuchi, Interpolating Blaschke products of type G, Complex Variables Theory Appl. 31 (1996), 51-64.
  • [20] C. Guillory, K. Izuchi and D. Sarason, Interpolating Blaschke products and division in Douglas algebras, Proc. Roy. Irish Acad. Sect. A 84 (1984), 1-7.
  • [21] K. Hoffman, Analytic functions and logmodular Banach algebras, Acta Math. 108 (1962), 271-317.
  • [22] K. Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. 86 (1967), 74-111.
  • [23] G. M. Leibowitz, Lectures on Complex Function Algebras, Scott, Foresman & Co. Glenview, IL, 1970.
  • [24] D. E. Marshall, Subalgebras of $L^∞$ containing $H^∞$, Acta Math. 137 (1976), 91-98.
  • [25] R. Mortini and V. Tolokonnikov, Blaschke products of Sundberg-Wolff type, Complex Variables Theory Appl. 30 (1996), 373-384.
  • [26] N. K. Nikol'skiĭ, Treatise on the Shift Operator, Springer, New York, 1985.
  • [27] D. Sarason, Algebras of functions on the unit circle, Bull. Amer. Math. Soc. 79 (1973), 286-299.
  • [28] D. Sarason, Algebras between $L^∞$ and $H^∞$, in: Spaces of Analytic Functions, Lecture Notes in Math. 512, Springer, 1976, 117-129.
  • [29] C. Sundberg and T. Wolff, Interpolating sequences for $QA_B$, Trans. Amer. Math. Soc. 276 (1983), 551-581.
  • [30] A. Volberg, Two remarks concerning the theorem of S. Axler, S.-Y. A. Chang, and D. Sarason, J. Operator Theory 8 (1982), 209-218.
  • [31] R. Younis and D. Zheng, Algebras generated by bounded analytic and harmonic functions and applications, preprint.
  • [32] D. Zheng, The distribution function inequality and products of Toeplitz operators and Hankel operators, J. Funct. Anal. 138 (1996), 477-501.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv127i3p201bwm
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