Isomorphism of certain weak $L^{p}$ spaces

• Autorzy: Denny H. Leung
• Języki publikacji: EN

Abstrakty

EN

It is shown that the weak $L^p$ spaces $ℓ^{p,∞}, L^{p,∞}[0,1]$, and $L^{p,∞}[0,∞)$ are isomorphic as Banach spaces.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 104
• Numer: 2
• Strony: 151-160

Daty

wydano

1993

otrzymano

1992-04-16

Twórcy

autor

Denny H. Leung

• Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511, Republic of Singapore

Bibliografia

• [1] N. L. Carothers and S. J. Dilworth, Subspaces of $L_p,q$, Proc. Amer. Math. Soc. 104 (1988), 537-545.
• [2] D. H. Leung, $L^{p,∞}$ has a complemented subspace isomorphic to $ℓ^2$, Rocky Mountain J. Math. 22 (1992), 943-952.
• [3] D. H. Leung, Embedding $L^{p,∞}$ into $L^{p,∞}[0,1]$ complementably, Bull. London Math. Soc. 23 (1991), 583-586.
• [4] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, Berlin 1977.
• [5] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II. Function Spaces, Springer, Berlin 1979.