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

A theorem on isotropic spaces

Félix Cabello Sánchez (1999)

Studia Mathematica

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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

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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.

Generalized versions of Ilmanen lemma: Insertion of C 1 , ω or C loc 1 , ω functions

Václav Kryštof (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove that for a normed linear space X , if f 1 : X is continuous and semiconvex with modulus ω , f 2 : X is continuous and semiconcave with modulus ω and f 1 f 2 , then there exists f C 1 , ω ( X ) such that f 1 f f 2 . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ω ( t ) = t ) to the case of an arbitrary nontrivial modulus ω . This generalization (where a C l o c 1 , ω function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.

On C * -spaces

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

Matematički Vesnik

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A generalized Kahane-Khinchin inequality

S. Favorov (1998)

Studia Mathematica

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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 .

A Marchaud type inequality

Jorge Bustamante (2022)

Commentationes Mathematicae Universitatis Carolinae

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We present a new Marchaud type inequality in 𝕃 p spaces.

On almost everywhere differentiability of the metric projection on closed sets in l p ( n ) , 2 < p <

Tord Sjödin (2018)

Czechoslovak Mathematical Journal

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Let F be a closed subset of n and let P ( x ) denote the metric projection (closest point mapping) of x n onto F in l p -norm. A classical result of Asplund states that P is (Fréchet) differentiable almost everywhere (a.e.) in n in the Euclidean case p = 2 . We consider the case 2 < p < and prove that the i th component P i ( x ) of P ( x ) is differentiable a.e. if P i ( x ) x i and satisfies Hölder condition of order 1 / ( p - 1 ) if P i ( x ) = x i .