Abstract
We find some necessary conditions for a real Banach space to be an almost CL-space. We also discuss the stability of CL-spaces and almost CL-spaces byc 0- andl 1-sums. Finally, we address the question if a space of vector-valued continuous functions can be a CL-space or an almost CL-space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Alfsen, E. andEffros, E., Structure in real Banach spaces.Ann. of Math. 96 (1972), 98–173.
Bonsall, F. F. andDuncan, J.,Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Math. Soc. Lecture Note Ser.2, Cambridge Univ. Press. London-New York. 1971.
Bonsall, F. F. andDuncan, J.,Numerical Ranges II. London Math. Soc. Lecture Note Ser.10, Cambridge Univ. Press. London-New York, 1973.
Duncan, J., McGregor, C. M., Pryce, J. D. andWhite, A. J., The numerical index of a normed space,J. London Math. Soc. 2 (1970), 481–488.
Fonf, V. P., Weakly extremal properties of Banach spaces.Mat. Zametki 45:6 (1989). 83–92, 112 (Russian). English transl.:Math. Notes 45 (1989), 488–494.
Fullerton, R. E., Geometrical characterizations of certain function spaces. inProc. Internat. Sympos. Linear spaces (Jerusalem, 1960), pp. 227–236, Jerusalem Academic Press, Jerusalem; Pergamon Press, Oxford, 1961.
Godefroy, G., Boundaries of a convex set and interpolation sets,Math. Ann. 277 (1987), 173–184.
Hanner, O., Intersections of translates of convex bodies.Math. Scand. 4 (1956), 65–87.
Hansen, A. B. andLima, Å., The structure of finite dimensional Banach spaces with the 3.2. intersection property.Acta Math. 146 (1981), 1–23.
Lacey, H. E.,The Isometric Theory of Classical Banach Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1974.
Lima, Å., Intersection properties of balls and subspaces in Banach spaces,Trans. Amer. Math. Soc. 227 (1977), 1–62.
Lima, Å., Intersection properties of balls in spaces of compact operators,Ann. Inst. Fourier (Grenoble) 28:3 (1978), 35–65.
Lima, Å., On extreme operators on finite-dimensional Banach spaces whose unit balls are polytopes,Ark. Mat. 19 (1981), 97–116.
Lindenstrauss, J.,Extension of Compact Operators, Mem. Amer. Math. Soc.48, Amer. Math. Soc., Providence, R. I., 1964.
Lindenstrauss, J. andTzafriri, L.,Classical Banach Spaces I: Sequence Spaces, Springer-Verlag, Berlin-New York, 1977.
López, G., Martín, M. andPayá, R., Real Banach spaces with numerical index 1,Bull. London Math. Soc. 31 (1999), 207–212.
Martín, M., A survey on the numerical index of a Banach space, inIII Congress on Banach Spaces (Jarandilla de la Vera, 1998). Extracta Math.15. pp. 265–276, Universidad de Extremadura, Departamento de Matemáticas, Badajoz, 2000.
Martín, M. andPayá, R., Numerical index of vector-valued function spaces,Studia Math. 142 (2000), 269–280.
Reisner, S., Certain Banach spaces associated with graphs and CL-spaces with 1-unconditional bases,J. London Math. Soc. 43 (1991), 137–148.
Ruess, W. M. andStegall, C. P., Extreme points in duals of operator spaces,Math. Ann. 261 (1982), 535–546.
Author information
Authors and Affiliations
Additional information
Research partially supported by Spanish MCYT project no. BFM2000-1467.
Rights and permissions
About this article
Cite this article
Martín, M., Payá, R. On CL-spaces and almost CL-spaces. Ark. Mat. 42, 107–118 (2004). https://doi.org/10.1007/BF02432912
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02432912