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Article

Keywords:
reproducing kernels; universal interpolating sequences; Bessel sequence; Riesz-Fischer sequence
Summary:
Let $H(K)$ be the Hilbert space with reproducing kernel $K$. This paper characterizes some sufficient conditions for a sequence to be a universal interpolating sequence for $H(K)$.
References:
[1] G. T.  Adams, P. J.  McGuire and V. I.  Paulsen: Analytic reproducing kernels and multiplication operators. Illinois J.  Math. 36 (1992), 404–419. MR 1161974
[2] N.  Aronszajn: Theory of reproducing kernels. Trans. Amer. Math. Soc. 68 (1950), 337–404. DOI 10.1090/S0002-9947-1950-0051437-7 | MR 0051437 | Zbl 0037.20701
[3] N.  Bari: Biorthogonal systems and bases in Hilbert space. Matematika 4 (1951), 69–107 (in Russian). MR 0050171
[4] J. B.  Conway: The Theory of Subnormal Operators. Math. Surveys Monographs  36. Amer. Math. Soc., , 1991. MR 1112128
[5] R. G.  Douglas: Banach Algebra Techniques in Operator Theory. Academic Press, New York, 1972. MR 0361893 | Zbl 0247.47001
[6] J. B.  Garnet: Bounded Analytic Functions. Academic Press, New York, 1981. MR 0628971
[7] I.  Schur: Bemerkungen zur Theorie der beschrönkten Biline arformen mit undendlich vielen Veränderlichen. Journal für die Reine und Angewandte Mathematik 140 (1911), 1–28.
[8] K.  Seddighi: Operators Acting on Hilbert Spaces of Analytic Functions. A series of lectures. Dept. of  Math., Univ. of Calgary, , 1991.
[9] K.  Seddighi and S. M.  Vaezpour: Commutants of certain multiplication operators on Hilbert spaces of analytic functions. Studia Mathematica 133 (1999), 121–130. MR 1686692
[10] H. S.  Shapiro and A. L.  Shields: On some interpolation problems for analytic functions. Amer. J.  Math. 83 (1961), 513–532. DOI 10.2307/2372892 | MR 0133446
[11] B.  Yousefi: Interpolating sequence on certain Banach spaces of analytic functions. Bull. Austral. Math. Soc. 65 (2002), 177–182. DOI 10.1017/S0004972700020219 | MR 1898531 | Zbl 1045.47024
[12] K.  Zhu: Operator Theory in Function Spaces. Marcel Dekker, New York, 1990. MR 1074007 | Zbl 0706.47019
[13] K.  Zhu: A class of operators associated with reproducing kernels. J.  Operator Theory 38 (1997), 19–24. MR 1462013 | Zbl 0892.47030
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