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1993 | 104 | 1 | 75-89
Tytuł artykułu

Isometries of Musielak-Orlicz spaces II

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EN
A characterization of isometries of complex Musielak-Orlicz spaces $L_Φ$ is given. If $L_Φ$ is not a Hilbert space and $U : L_Φ → L_Φ$ is a surjective isometry, then there exist a regular set isomorphism τ from (T,Σ,μ) onto itself and a measurable function w such that U(f) = w ·(f ∘ τ) for all $f ∈ L_Φ$. Isometries of real Nakano spaces, a particular case of Musielak-Orlicz spaces, are also studied.
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Twórcy
  • Department of Mathematics, Memphis State University, Memphis, Tennessee 38152, U.S.A.
autor
  • Department of Mathematics, Memphis State University, Memphis, Tennessee 38152, U.S.A.
autor
  • Department of Mathematics, Memphis State University, Memphis, Tennessee 38152, U.S.A.
Bibliografia
  • [1] S. Banach, Theory of Linear Operations, North-Holland, 1987.
  • [2] E. Berkson and H. Porta, Hermitian operators and one-parameter groups of isometries in Hardy spaces, Trans. Amer. Math. Soc. 185 (1973), 331-344.
  • [3] F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Math. Soc. Lecture Note Ser. 2, Cambridge University Press, 1971.
  • [4] R. Fleming and J. E. Jamison, Isometries on certain Banach spaces, J. London Math. Soc. (2) 9 (1974), 363-371.
  • [5] R. Fleming, J. E. Jamison and A. Kamińska, Isometries of Musielak-Orlicz spaces, in: Proceedings of the Conference on Function Spaces, Edwardsville 1990, Marcel Dekker, 1992, 139-154.
  • [6] J. E. Jamison and I. Loomis, Isometries of Orlicz spaces of vector valued functions, Math. Z. 193 (1986), 363-371.
  • [7] N. J. Kalton and G. V. Wood, Orthonormal systems in Banach spaces and their applications, Math. Proc. Cambridge Philos. Soc. 79 (1976), 493-510.
  • [8] A. Kamińska, Some convexity properties of Musielak-Orlicz spaces of Bochner type, Rend. Circ. Mat. Palermo (2) Suppl. 10 (1985), 63-73.
  • [9] A. Kamińska, Isometries of Orlicz spaces equipped with the Orlicz norm, Rocky Mountain J. Math., to appear.
  • [10] W. Kozlowski, Modular Function Spaces, Marcel Dekker, New York 1988.
  • [11] M. A. Krasnosel'skiǐ and Ya. B. Rutickiǐ, Convex Functions and Orlicz Spaces, Noordhoff, Groningen 1961.
  • [12] G. Lumer, On the isometries of reflexive Orlicz spaces, Ann. Inst. Fourier (Grenoble) 13 (1) (1963), 99-109.
  • [13] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, 1983.
  • [14] H. Nakano, Topology and Linear Spaces, Nihonbashi, Tokyo 1951.
  • [15] A. R. Sourour, The isometries of $L^p (Ω,X)$, J. Funct. Anal. 30 (1978), 276-285.
  • [16] M. G. Zaǐdenberg, Groups of isometries of Orlicz spaces, Soviet Math. Dokl. 17 (1976), 432-436.
  • [17] M. G. Zaǐdenberg, On isometric classification of symmetric spaces, ibid. 18 (1977), 636-640.
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Bibliografia
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