Search results for "REFLEX"

Shrinking and boundedly complete Schauder frames in Fréchet spaces

2014

We study Schauder frames in Fréchet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete Schauder frames on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. We characterize when an unconditional Schauder frame is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete Schauder frames in function spaces are also presented.

Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings

2006

Abstract It is shown that if the modulus Γ X of nearly uniform smoothness of a reflexive Banach space satisfies Γ X ′ ( 0 ) 1 , then every bounded closed convex subset of X has the fixed point property for nonexpansive mappings. In particular, uniformly nonsquare Banach spaces have this property since they are properly included in this class of spaces. This answers a long-standing question in the theory.

Best proximity points: Convergence and existence theorems for p-cyclic mappings

2010

Abstract We introduce a new class of mappings, called p -cyclic φ -contractions, which contains the p -cyclic contraction mappings as a subclass. Then, convergence and existence results of best proximity points for p -cyclic φ -contraction mappings are obtained. Moreover, we prove results of the existence of best proximity points in a reflexive Banach space. These results are generalizations of the results of Al-Thagafi and Shahzad (2009) [8] .

The Bishop–Phelps–Bollobás theorem for operators

2008

AbstractWe prove the Bishop–Phelps–Bollobás theorem for operators from an arbitrary Banach space X into a Banach space Y whenever the range space has property β of Lindenstrauss. We also characterize those Banach spaces Y for which the Bishop–Phelps–Bollobás theorem holds for operators from ℓ1 into Y. Several examples of classes of such spaces are provided. For instance, the Bishop–Phelps–Bollobás theorem holds when the range space is finite-dimensional, an L1(μ)-space for a σ-finite measure μ, a C(K)-space for a compact Hausdorff space K, or a uniformly convex Banach space.

On the Zero-Set of Real Polynomials in Non-Separable Banach Spaces

2007

We show constructively that every homogeneous polynomial that is weakly continuous on the bounded subsets of a real Banach space whose dual is not weak ∗ separable admits a closed linear subspace whose dual is not weak ∗ -separable either where the polynomial vanishes. We also prove that the same can be said for vectorvalued polynomials. Finally, we study the validity of this result for continuous 2homogeneous polynomials.

On the stability of the Bohl — Brouwer — Schauder Theorem

1996

A note on the closed graph theorem

1977

Weakly continuous mappings on Banach spaces

1983

Abstract It is shown that every n -homogeneous continuous polynomial on a Banach space E which is weakly continuous on the unit ball of E is weakly uniformly continuous on the unit ball of E . Applications of the result to spaces of polynomials and holomorphic mappings on E are given.

Specific modulation of corticospinal and spinal excitabilities during maximal voluntary isometric, shortening and lengthening contractions in synergi…

2011

Non-technical summary  The neural control of muscle activity differs during voluntary shortening and lengthening contractions. In this paper, we show that the relative contribution of both cortical and spinal mechanisms to the modulation of neural activation is specific during lengthening contraction and differs between synergist muscles. Knowledge of spinal and corticospinal excitabilities modulations during shortening and lengthening muscle contraction improves our understanding of the processes that underlies the neural control of muscles during dynamic contractions.

Suppressive Efficacy by a Commercially Available Blue Lens on PPR in 610 Photosensitive Epilepsy Patients

2006

Purpose Photosensitivity can represent a serious problem in epilepsy patients, also because pharmacologic treatment is often ineffective. Nonpharmacologic treatment using blue sunglasses is effective and safe in controlling photosensitivity, but large series of patients have never been studied. Methods This multicenter study was conducted in 12 epilepsy centers in northern, central, southern, and insular Italy. A commercially available lens, named Z1, obtained in a previous trial, was used to test consecutively enrolled pediatric and adult epilepsy patients with photosensitivity. Only type 4 photosensitivity (photoparoxysmal response, PPR) was considered in the study. A standardized method …