Fatou's Lemma and the Lebesgue's Convergence Theorem
In this article we prove the Fatou's Lemma and Lebesgue's Convergence Theorem [10].MML identifier: MESFUN10, version: 7.9.01 4.101.1015
Finite codimensional linear isometries on spaces of differentiable and Lipschitz functions
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 dimensional projection constants
Finite dimensional subspaces of
Finite rank approximation and semidiscreteness for linear operators
Given a completely bounded map from an operator space into a von Neumann algebra (or merely a unital dual algebra) , we define to be -semidiscrete if for any operator algebra , the tensor operator is bounded from into , with norm less than . 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...
Finite representability of the Yang operator.
Finite-dimensional Banach spaces with numerical index zero.
Finite-dimensional Banach spaces with symmetry constant of order √n
Finite-dimensional decompositions of Banach spaces with (p,q)-estimates [Book]
Finite-dimensional subspaces of uniformly convex and uniformly smooth Banach lattices and trace classes
First class selectors for weakly upper semi-continuous multi-valued maps in Banach spaces.
First results on spectrally bounded operators
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.
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 generalized Lipschitzian semigroups in Banach spaces.
Fixed point theorems for nonexpansive mappings in modular spaces
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 is a convex, -complete modular space satisfying the Fatou property and -uniformly convex for all , C a convex, -closed, -bounded subset of , a -nonexpansive mapping, then has a fixed point.
Fixed point theorems in cone Banach spaces.
Fixed points and random stability of a generalized Apollonius type quadratic functional equation.
Fixed points and stability for functional equations in probabilistic metric and random normed spaces.
Fixed points of asymptotically regular mappings in spaces with uniformly normal structure
It is proved that: for every Banach space which has uniformly normal structure there exists a with the property: if is a nonempty bounded closed convex subset of and is an asymptotically regular mapping such that where is the Lipschitz constant (norm) of , then has a fixed point in .
FK-espaces contenant c0 en analyse non-archimédienne.