On the spectra of certain Laurent operators on Orlicz spaces
W. Luxemburg (1968)
Studia Mathematica
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W. Luxemburg (1968)
Studia Mathematica
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Shutao Chen, Huiying Sun (1994)
Studia Mathematica
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We prove that an Orlicz space equipped with the Luxemburg norm has uniformly normal structure if and only if it is reflexive.
Yunan Cui, Henryk Hudzik, Wang Ping (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Neil Trudinger (1974)
Studia Mathematica
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D. Fernandez, J. Garcia (1991)
Studia Mathematica
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Boris Godunov, Petr Zabreĭko (1995)
Studia Mathematica
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We discuss the problem of characterizing the possible asymptotic behaviour of the iterates of a sufficiently smooth nonlinear operator acting in a Banach space in small neighbourhoods of a fixed point. It turns out that under natural conditions, for the most part of initial approximations these iterates tend to "lie down" along a finite-dimensional subspace generated by the leading (peripherical) eigensubspaces of the Fréchet derivative at the fixed point and moreover the asymptotic...
S. Kwapień (1968)
Studia Mathematica
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J. Uhl (1971)
Studia Mathematica
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W. Evans, D. Harris, J. Lang (1998)
Studia Mathematica
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In [2] and [3] upper and lower estimates and asymptotic results were obtained for the approximation numbers of the operator defined by when 1 < p < ∞. Analogous results are given in this paper for the cases p = 1,∞ not included in [2] and [3].
Zhongdao Ren, Shutao Chen (1997)
Collectanea Mathematica
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Estimation of the Jung constants of Orlicz function spaces equipped with either Luxemburg norm or Orlicz norm is given. The exact values of the Jung constants of a class of reflexive Orlicz function spaces have been found by using a new quantitative index of N-functions.
Ye Yining, Huang Yafeng (1993)
Collectanea Mathematica
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We prove that in the Musielak-Orlicz sequence spaces equipped with the Luxemburg norm, P-convexity coincides with reflexivity.