Linear Operators and Vector Measures. II.
Linear operators in the space of regulated functions
Representation of bounded and compact linear operators in the Banach space of regulated functions is given in terms of Perron-Stieltjes integral.
Linear operators on
Linear operators on for dispersed
Linear operators on and Lorentz spaces: The Krasnosel’skii-Zabrieko characteristic sets
Linear operators on non-locally convex Orlicz spaces
We study linear operators from a non-locally convex Orlicz space to a Banach space . Recall that a linear operator is said to be σ-smooth whenever in implies . It is shown that every σ-smooth operator factors through the inclusion map , where Φ̅ denotes the convex minorant of Φ. We obtain the Bochner integral representation of σ-smooth operators . This extends some earlier results of J. J. Uhl concerning the Bochner integral representation of linear operators defined on a locally convex...
Linear preservers on ℬ(X)
Linearization and compactness
This paper is devoted to several questions concerning linearizations of function spaces. We first consider the relation between linearizations of a given space when it is viewed as a function space over different domains. Then we study the problem of characterizing when a Banach function space admits a Banach linearization in a natural way. Finally, we consider the relevance of compactness properties in linearizations, more precisely, the relation between different compactness properties of a mapping,...
Lipschitz continuity in Muckenhoupt 𝓐₁ weighted function spaces
We study continuity envelopes of function spaces and where the weight belongs to the Muckenhoupt class ₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.
Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures.
In the setting of a metric measure space (X, d, μ) with an n-dimensional Radon measure μ, we give a necessary and sufficient condition for the boundedness of Calderón-Zygmund operators associated to the measure μ on Lipschitz spaces on the support of μ. Also, for the Euclidean space Rd with an arbitrary Radon measure μ, we give several characterizations of Lipschitz spaces on the support of μ, Lip(α,μ), in terms of mean oscillations involving μ. This allows us to view the "regular" BMO space of...
Lipschitzian norm estimate of one-dimensional Poisson equations and applications
By direct calculus we identify explicitly the lipschitzian norm of the solution of the Poisson equation in terms of various norms of g, where is a Sturm–Liouville operator or generator of a non-singular diffusion in an interval. This allows us to obtain the best constant in the L1-Poincaré inequality (a little stronger than the Cheeger isoperimetric inequality) and some sharp transportation–information inequalities and concentration inequalities for empirical means. We conclude with several illustrative...
Little G. T. for lp-lattice summing operators
2000 Mathematics Subject Classification: 46B28, 47D15.In this paper we introduce and study the lp-lattice summing operators in the category of operator spaces which are the analogous of p-lattice summing operators in the commutative case. We study some interesting characterizations of this type of operators which generalize the results of Nielsen and Szulga and we show that Λ l∞( B(H) ,OH) ≠ Λ l2( B( H) ,OH), in opposition to the commutative case.
Littlewood functions, Hankel multipliers and power bounded operators on a Hilbert space
Littlewood-Paley theory and ϵ-families of operators
Local entropy moduli and eigenvalues of operators in Banach spaces.
In the paper local entropy moduli of operators between Banach spaces are introduced. They constitue a generalization of entropy numbers and moduli, and localize these notions in an appropriate way. Many results regarding entropy numbers and moduli can be carried over to local entropy moduli. We investigate relations between local entropy moduli and s-numbers, spectral properties, eigenvalues, absolutely summing operators. As applications, local entropy moduli of identical and diagonal operators...
Local Operators Between Spaces of Ultradifferentiable Functions and Ultradistributions.
Local Reflexivity and (p, g)-Summing Maps.
Local spectral radius formula for operators in Banach spaces
Local spectral theory of shifts with operator-valued weights. (Sur la théorie spectrale locale des shifts à poids opérateurs.)
Local spectrum and Kaplansky's theorem on algebraic operators
Using elementary arguments we improve former results of P. Vrbová concerning local spectrum. As a consequence, we obtain a new proof of Kaplansky’s theorem on algebraic operators on a Banach space.