Properly semi-L-embedded complex spaces

• Autorzy: Angel Rodríguez Palacios
• Języki publikacji: EN

Abstrakty

EN

We prove the existence of complex Banach spaces X such that every element F in the bidual X** of X has a unique best approximation π(F) in X, the equality ∥F∥ = ∥π (F)∥ + ∥F - π (F)∥ holds for all F in X**, but the mapping π is not linear.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 106
• Numer: 2
• Strony: 197-202

Daty

wydano

1993

otrzymano

1992-11-17

poprawiono

1993-02-21

Twórcy

autor

Angel Rodríguez Palacios

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain,

Bibliografia

• [1] C. Aparicio, F. Ocaña, R. Payá and A. Rodríguez, A non-smooth extension of Fréchet differentiability of the norm with applications to numerical ranges, Glasgow Math. J. 28 (1986), 121-137.
• [2] T. J. Barton and R. M. Timoney, Weak* continuity of Jordan triple products and applications, Math. Scand. 59 (1986), 177-191.
• [3] E. Behrends, Points of symmetry of convex sets in the two-dimensional complex space. A counterexample to D. Yost's problem, Math. Ann. 290 (1991), 463-471.
• [4] E. Behrends and P. Harmand, Banach spaces which are proper M-ideals, Studia Math. 81 (1985), 159-169.
• [5] P. Harmand and Å. Lima, Banach spaces which are M-ideals in their biduals, Trans. Amer. Math. Soc. 283 (1983), 253-264.
• [6] P. Harmand and T. S. S. R. K. Rao, An intersection property of balls and relations with M-ideals, Math. Z. 197 (1988), 277-290.
• [7] P. Harmand, D. Werner and W. Werner, M-ideals in Banach Spaces and Banach Algebras, Lecture Notes in Math., Springer, to appear.
• [8] Å. Lima, Intersection properties of balls and subspaces of Banach spaces, Trans. Amer. Math. Soc. 229 (1977), 1-62.
• [9] J. Martínez, J. F. Mena, R. Payá and A. Rodríguez, An approach to numerical ranges without Banach algebra theory, Illinois J. Math. 29 (1985), 609-626.
• [10] J. F. Mena, R. Payá and A. Rodríguez, Absolute subspaces of Banach spaces, Quart. J. Math. Oxford 40 (1989), 43-64.
• [11] R. Payá and A. Rodríguez, Banach spaces which are semi-M-summands in their biduals, Math. Ann. 289 (1991), 529-542.
• [12] D. Yost, Semi-M-ideals in complex Banach spaces, Rev. Roumaine Math. Pures Appl. 29 (1984), 619-623.