On an extension of norms from a subspace to the whole Banach space keeping their rotundity

• Autorzy: M. Fabian
• Języki publikacji: EN

Abstrakty

EN

Let ℛ denote some kind of rotundity, e.g., the uniform rotundity. Let X admit an ℛ-norm and let Y be a reflexive subspace of X with some ℛ-norm ∥·∥. Then we are able to extend ∥·∥ from Y to an ℛ-norm on X.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994-1995
• Tom: 112
• Numer: 3
• Strony: 203-211

Daty

wydano

1995

otrzymano

1993-03-03

Twórcy

autor

M. Fabian

• Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

Bibliografia

• [1] J. M. Borwein and M. Fabian, On convex functions having points of Gateaux differentiability which are not points of Fréchet differentiability, a preprint.
• [2] J. M. Borwein, M. Fabian and J. Vanderwerff, Locally Lipschitz functions and bornological derivatives, a preprint.
• [3] J. Diestel, Geometry of Banach Spaces-Selected Topics, Lecture Notes in Math. 485, Springer, 1975.
• [4] R. Deville, G. Godefroy and V. E. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs in Pure and Appl. Math. 64, Wiley, New York, 1993.
• [5] K. John and V. Zizler, On extension of rotund norms, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 705-707.
• [6] K. John and V. Zizler, On extension of rotund norms II, Pacific J. Math. 82 (1979), 451-455.
• [7] V. E. Zizler, Smooth extension of norms and complementability of subspaces, Arch. Math. (Basel) 53 (1989), 585-589.