M-ideal properties in Marcinkiewicz spaces

• Autorzy: Kamińska A. , Lee H. J.
• Języki publikacji: EN

Abstrakty

EN

We study M-ideal properties of function and sequence Marcinkiewicz spaces. In particular we calculate the duals of the space L - L1 + L°° equipped with two standard norms and investigate when its subspace of order continuous elements is an M-ideal in E.

Słowa kluczowe

EN

M-ideals; Marcinkiewicz spaces; weak Lorentz spaces; L^1+ L°° spaces

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr spec.
• Strony: 123--144
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Kamińska A.

• Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, USA

autor

Lee H. J.

• Department of Mathematics, Korea Advanced Institute of Science and Technology, 373-1, Kusong-Dong, Yusong-Gu, Taejon, 305-701, Republic of Korea

Bibliografia

• [1] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, 1988.
• [2] P. Harmand, D. Werner and W. Werner, M-ideals in Banach Spaces and Banach Algebras, Lecture Notes in Mathematics 1547, Springer-Verlag, 1993.
• [3] H. Hudzik, A. Kamińska and M. Mastyło, Local geometry of L1 ∩ L∞ and L1 + L∞, Arch. Math. 68 (1997), 159-168.
• [4] A. Kamińska and M. Mastyło, The Dunford Pettis property for symmetric spaces, Canad. J. Math 52 (4) (2000), 789-803.
• [5] S. G. Krein, Ju. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, AMS Translations of Math. Monog. 54, 1982.
• [6] W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces II, North-Holland, Amsterdam, 1983.
• [7] M. Väth, Ideal Spaces, Lecture Notes in Mathematics 1664, Springer-Verlag, 1997.
• [8] A. C. Zaanen, Introduction to Operator Theory in Riesz Spaces, Springer-Verlag, 1997.

Uwagi

Dedicated to Professor Julian Musielak on his 75th birthday.