Search results for "Lp space"
showing 8 items of 58 documents
Common fixed point results on quasi-Banach spaces and integral equations
2013
In this paper we obtain fixed and common fixed point theorems for self-mappings defined on a closed and convex subset C of a quasi-Banach space. We give also a constructive method for finding the common fixed points of the involved mappings. As an application we obtain a result of the existence of solutions of integral equations.
Norm continuity and related notions for semigroups on Banach spaces
1996
We find some conditions on a c0-semigroup on a Banach space and its resolvent connected with the norm continuity of the semigroup. We use them to get characterizations of norm continuous, eventually norm continuous and eventually compact semigroups on Hilbert spaces in terms of the growth of the resolvent of their generator.
Embedding of Sobolev Spaces into Lipschitz Spaces
1989
The main result of the paper is that if Ω is a bounded uniform domain in ℝn and p>n, then the Sobolev space Wl, p(Ω) embeds continously into Cα(Ω), α = 1 - n/p.
Implementability of Liouville Evolution, Koopman and Banach-Lamperti Theorems in Classical and Quantum Dynamics
2002
We extend the concept of implementability of semigroups of evolution operators associated with dynamical systems to quantum case. We show that such an extension can be properly formulated in terms of Jordan morphisms and isometries on non-commutative Lp spaces. We focus our attention on a non-commutative analog of the Banach-Lamperti theorem.
A note on Malliavin smoothness on the Lévy space
2017
We consider Malliavin calculus based on the Itô chaos decomposition of square integrable random variables on the Lévy space. We show that when a random variable satisfies a certain measurability condition, its differentiability and fractional differentiability can be determined by weighted Lebesgue spaces. The measurability condition is satisfied for all random variables if the underlying Lévy process is a compound Poisson process on a finite time interval. peerReviewed
Operator martingale decomposition and the Radon-Nikodym property in Banach spaces
2010
Abstract We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon–Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney–Schaefer l-tensor product E ⊗ ˜ l Y , where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon–Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on E ⊗ ˜ l Y . Secondly, we derive a Riesz decomposition for uniform …
Geometric mean and triangles inscribed in a semicircle in Banach spaces
2008
AbstractWe consider the triangles with vertices x, −x and y where x,y are points on the unit sphere of a normed space. Using the geometric means of the variable lengths of the sides of these triangles, we define two geometric constants for Banach spaces. These constants are closely related to the modulus of convexity of the space under consideration, and they seem to represent a useful tool to estimate the exact values of the James and Jordan–von Neumann constants of some Banach spaces.
Characterizations of convex approximate subdifferential calculus in Banach spaces
2016
International audience; We establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding conjugates, with respect to any given topology intermediate between the norm and the weak* topologies on the dual space. Such a condition turns out to also be necessary in Banach spaces. These results extend both the classical formulas by Hiriart-Urruty and Phelps and by Thibault.