Related papers: Structure theory for maximally monotone operators …
In this paper we prove that maximal H-monotone operators $T:H^n\rightrightarrows V_1$ whose domain is all the Heisenberg group $H^n$ are locally bounded. This implies that they are upper semicontinuous. As a consequence, maximal…
We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fr\'{e}chet space of the entire mappings that are bounded on bounded sets the composition turns to be…
We present a simple proof of the maximal monotonicity of the subdifferential operator in general Banach spaces. Using the Fitzpatrick function the Rockafellar surjectivity theorem follows as a corollary.
Our aim in this paper is to present results of existence of fixed points for continuous operators in Banach spaces using measure of noncompactness under an integral condition. This results are generalization of results given by A. Aghajania…
Motivated by the equivalent definition of a continuous operator between Banach spaces in terms of weakly null nets, we introduce two types of continuous operators between Banach lattices using unbounded absolute weak convergence. We…
In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity…
In this note we answer positively to two conjectures proposed by Nieraeth (2023) about the maximal operator on rescaled Banach function spaces. We also obtain a new criterion saying when the maximal operator bounded on a Banach function…
We present a new sufficient condition under which a maximal monotone operator $T:X\tos X^*$ admits a unique maximal monotone extension to the bidual $\widetilde T:X^{**} \rightrightarrows X^*$. For non-linear operators this condition is…
In this paper, we first give some new characterizations of Muckenhoupt type weights through establishing the boundedness of maximal operators on the weighted Lorentz and Morrey spaces. Secondly, we establish the boundedness of sublinear…
We provide a concise proof of existence for nonlinear operator equations in separable Banach spaces. Notably, the operator is not assumed to be monotone. Instead, our main hypotheses consist of a continuity assumption and a generalized…
Motivated by a seminal paper of professor M. Z. Nashed published in 1987 on classification of ill-posed linear operator equations and distinguishing two types of ill-posedness in Banach and Hilbert spaces, we present, illustrate and justify…
We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…
We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X --> X such that the set A = {x in X : ||R^n(x)|| --> infinity} is non-empty and nowhere dense in X. Moreover, if…
We establish the weak Banach-Saks property for function spaces arising as the optimal domain of an operator.
The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar's constraint qualification holds, which is called the "sum…
We study differentiability properties of convex operators defined on a Banach space with values in an $\Lc_p$ space and of their compositions with monotonic convex functionals on this space. We develop new tools for operators enjoying an…
We prove several abstract results giving general conditions under which subspaces of linear or multilinear operators on Banach spaces or Banach lattices are closed. Each of these abstract results is followed by concrete applications,…
We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to…
We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces $H(p,q,\alpha)$. First, we study the separable spaces $H(p,q,\alpha)$ with $q<\infty,$ that behave as the Hardy and Bergman…
We consider the Banach space $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ of bounded analytic functions on the open right half-plane $\mathbb{C}_0$ that are almost periodic on some smaller half-plane, as well as the subspace…