Uniform λ-property in L¹∩L^∞

• Autorzy: Bohonos A. , Płuciennik R.

Identyfikatory

DOI

10.14708/cm.v55i2.1122

• Języki publikacji: EN

Abstrakty

EN

Here it is proved that the space L¹∩L^∞ equipped with the standard interpolation norm ∥⋅∥_L1∩L∞=max{∥⋅∥_L1,∥⋅∥_L∞} has the uniform λ-property if and only if μ(T)≤1. Replacing the standard norm with an equivalent one ∥⋅∥′_L1∩L∞= ∥⋅∥_L1+∥⋅∥_L∞, a different result is obtained.: (L¹∩L^∞,∥⋅∥′_L1∩L∞) has the uniform λ-property if and only if \(\mu (T)

Słowa kluczowe

EN

lambda property; uniform lambda property; interpolation space; convex series representation property

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2015
• Tom: Vol 55, No. 2
• Strony: 171--181
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Bohonos A.

• Schol of Mathematics, West Pomerian University of Technology, Al. Piastów 48/49, 70-310 Szczecin, Poland

autor

Płuciennik R.

• Institute of Mathematics, Poznań University of Technology; Piotrowo 3A, 60-965 Poznań, Poland

Bibliografia

• [1] R. M. Aron and R. H. Lohman, A geometric function determined by extreme points of the unit ball of a normed space, Pacific J. Math. 127 (1987), 209-231.
• [2] R. M. Aron, R. H. Lohman, and A. Suarez Granero, Rotundity, the C.S.R.P., and the X-property in Banach spaces, Proc. Amer. Math. Soc. Ill (1991), 151-155, DOI 10.2307/2047873.
• [3] C. Benett and R. Sharpley, Interpolation of Operators, Academic Press Inc., London-New York-San Francisco 1988.
• [4] G. Birkhoff, Lattice Theory, Providence, RI1967.
• [5] A. Bohonos and R. Płuciennik, X-property in Orlicz spaces, J. Convex Analysis 21 (2014), no. 1,147-166.
• [6] S. T. Chen, Geometry of Orlicz Spaces, Dissertation Math. 356 (1996), 1-204.
• [7] M. Ciesielski, On geometric structure of symmetric spaces,J. Math. Anal, and Appl. 430 (2015), no. 1, 98-125, DOI 10.1016/j.jmaa.2015.04.040.
• [8] M. Ciesielski, P. Kolwicz, and R. Płuciennik, Local approach to Kadec-Klee properties in symmetric function spaces, J. Math. Anal, and Appl. 426 (2015), no. 2, 700-726, DOI 10.1016/j.jmaa.2015.01.064.
• [9] Y. A. Cui, H. Hudzik, and R. Płuciennik, 2003, Z. Anal. Anwendungen 22, no. 4, 789-817, DOI 10.4171/ZAA/1174.
• [10] R. Grząślewicz, H. Hudzik, and W. Kurc, Extreme and exposed points in Orlicz spaces, Canad. J. Math 44 (1992), no. 3, 505-515, DOI 10.4153/CJM-1992-032-3.
• [11] H. Hudzik, A. Kamińska, and M. Mastyło, Monotonicity and rotundity properties in Banach lattices, Rocky Mountain J. Math. 30 (2000), no. 3, 933-949, DOI 10.1216/rmjm/1021477253.
• [12] S. G. Krein, Ju. I. Petunin, and E. M. Semenov, Interpolation of Linear Operators, AMS Trans, of Math. Monographs, vol. 54, Providence, R. 1.1982.
• [13] R. H. Lohman, The X-function in Banach spaces, Banach Space Theory, Contemp. Math., vol. 85, Amer. Math. Soc., Providence, R.I., 1989, 345-351.
• [14] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math., vol. 1034, Springer-Verlag 1983, 1-222.