Orthogonally complemented hyperplanes in Orlicz function spaces

• Autorzy: Chen S. , Hudzik H. , Wang Y.
• Języki publikacji: EN

Abstrakty

EN

In this paper, necessary and sufficient conditions for a closed hyperplane in Orlicz space to be generalized orthogonally complemented are given for both the Orlicz and the Luxemburg norm. The concept of strongly generalized orthogonally complemented subspace in Banach space is defined and criteria for such subspaces in Orlicz space for both norms are given.

Słowa kluczowe

EN

Orlicz space; Orlicz norm; orthogonally complemented hyperplane; duality mapping; support functional; James orthogonality

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr spec.
• Strony: 71--82
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Chen S.

• School of Mathematics and Computer Science, Harbin Normal University, Harbin, 150080, P.R. China

autor

Hudzik H.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

autor

Wang Y.

• School of Mathematics and Computer Science, Harbin Normal University, Harbin, 150080, P.R. China

Bibliografia

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• [6] J. Diestel, Geometry of Banach Spaces-Selected Topics, Springer-Verlag, 1975.
• [7] R. Grząślewicz and H. Hudzik, Smooth points of Orlicz spaces equipped with the Luxemburg norm, Math. Nachr. 155 (1992), 31-45.
• [8] H. Hudzik and Z. Zbąszyniak, Smoothness points of Musielak-Orlicz spaces equipped with the Orlicz norm, Collectanea Math. 48, 4-5-6 (1997), 543-561.
• [9] R. C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc. 61 (1947), 265-292.
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• [11] M. Z. Nashed, Ed. Generalized Inverse and Applications, Academic Press, New York, 1976.
• [12] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker Inc, New York, Basel, Hong-Kong, 1991.
• [13] Y. W. Wang and H. Wang, Generalized orthogonal decomposition theorem in Banach space and, generalized orthogonally complemented subspace, Acta Math. Sinica 44 (2001), 1045-1050.
• [14] Y. W. Wang and S. R. Pan, An approximation problem of the finite rank operator in Banach spaces, Science in China (Series A) 46 (2003), 245-250.
• [15] C. X. Wu, T. F. Wang, S. T. Chen and Y. W. Wang, Geometry of Orlicz Spaces, Harbin, 1986.
• [16] Z. Zbąszyniak, Smooth points of the unit spheres in Musielak-Orlicz function spaces equipped with the Luxemburg norm, Comment. Math. Univ. Carolinae 35 (1994), 95-102.

Uwagi

Dedicated to Professor Musielak on the occasion of his 75th birthday.