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Finite codimensional linear isometries on spaces of differentiable and Lipschitz functions

Hironao Koshimizu (2011)

Open Mathematics

We characterize finite codimensional linear isometries on two spaces, C (n)[0; 1] and Lip [0; 1], where C (n)[0; 1] is the Banach space of n-times continuously differentiable functions on [0; 1] and Lip [0; 1] is the Banach space of Lipschitz continuous functions on [0; 1]. We will see they are exactly surjective isometries. Also, we show that C (n)[0; 1] and Lip [0; 1] admit neither isometric shifts nor backward shifts.

Finite rank approximation and semidiscreteness for linear operators

Christian Le Merdy (1999)

Annales de l'institut Fourier

Given a completely bounded map u : Z → M from an operator space Z into a von Neumann algebra (or merely a unital dual algebra) M , we define u to be C -semidiscrete if for any operator algebra A , the tensor operator I A ⊗ u is bounded from A ⊗ min Z into A ⊗ nor M , with norm less than C . We investigate this property and characterize it by suitable approximation properties, thus generalizing the Choi-Effros characterization of semidiscrete von Neumann algebras. Our work is an extension of some recent work of Pisier on an analogous...

First results on spectrally bounded operators

M. Mathieu, G. J. Schick (2002)

Studia Mathematica

A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is defined to be spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ Mr(x) for all x ∈ E, where r(·) denotes the spectral radius. We study some basic properties of this class of operators, which are sometimes analogous to, sometimes very different from, those of bounded operators between Banach spaces.

Fixed point free maps of a closed ball with small measures of noncompactness.

Martin Väth (2001)

Collectanea Mathematica

We show that in all infinite-dimensional normed spaces it is possible to construct a fixed point free continuous map of the unit ball whose measure of noncompactness is bounded by 2. Moreover, for a large class of spaces (containing separable spaces, Hilbert spaces and l-infinity (S)) even the best possible bound 1 is attained for certain measures of noncompactness.

Fixed point theorems for nonexpansive mappings in modular spaces

Poom Kumam (2004)

Archivum Mathematicum

In this paper, we extend several concepts from geometry of Banach spaces to modular spaces. With a careful generalization, we can cover all corresponding results in the former setting. Main result we prove says that if ρ is a convex, ρ -complete modular space satisfying the Fatou property and ρ r -uniformly convex for all r > 0 , C a convex, ρ -closed, ρ -bounded subset of X ρ , T : C → C a ρ -nonexpansive mapping, then T has a fixed point.

Fixed points of asymptotically regular mappings in spaces with uniformly normal structure

Jarosław Górnicki (1991)

Commentationes Mathematicae Universitatis Carolinae

It is proved that: for every Banach space X which has uniformly normal structure there exists a k > 1 with the property: if A is a nonempty bounded closed convex subset of X and T : A → A is an asymptotically regular mapping such that lim inf n → ∞ | | | T n | | | < k , where | | | T | | | is the Lipschitz constant (norm) of T , then T has a fixed point in A .

Currently displaying 21 – 40 of 65