Displaying similar documents to “ L 1 contains every two-dimensional normed space”

A theorem on isotropic spaces

Félix Cabello Sánchez (1999)

Studia Mathematica


Let X be a normed space and G F ( X ) the group of all linear surjective isometries of X that are finite-dimensional perturbations of the identity. We prove that if G F ( X ) acts transitively on the unit sphere then X must be an inner product space.

On area and side lengths of triangles in normed planes

Gennadiy Averkov, Horst Martini (2009)

Colloquium Mathematicae


Let d be a d-dimensional normed space with norm ||·|| and let B be the unit ball in d . Let us fix a Lebesgue measure V B in d with V B ( B ) = 1 . This measure will play the role of the volume in d . We consider an arbitrary simplex T in d with prescribed edge lengths. For the case d = 2, sharp upper and lower bounds of V B ( T ) are determined. For d ≥ 3 it is noticed that the tight lower bound of V B ( T ) is zero.

On C * -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik


A generalized Kahane-Khinchin inequality

S. Favorov (1998)

Studia Mathematica


The inequality ʃ l o g | a n e 2 π i φ n | d φ 1 d φ n C l o g ( | a n | 2 ) 1 / 2 with an absolute constant C, and similar ones, are extended to the case of a n belonging to an arbitrary normed space X and an arbitrary compact group of unitary operators on X instead of the operators of multiplication by e 2 π i φ .