Related papers: Regularity Properties of Sectorial Operators: Coun…
We provide regularity of solutions to a large class of evolution equations on Banach spaces where the generator is composed of a static principal part plus a non-autonomous perturbation. Regularity is examined with respect to the graph norm…
We describe a subclass of the class of normal operators on Banach spaces over non-Archimedean fields (A. N. Kochubei, J. Math. Phys. 51 (2010), article 023526) consisting of operators whose properties resemble those of unitary operators. In…
We study the behaviour of linear partial differential operators with polynomial coefficients via a Wigner type transform. In particular, we obtain some results of regularity in the Schwartz space $\mathcal S$ and in the space ${\mathcal…
In terms of triples of Banach spaces, we define a large class of boundary problems for ordinary differential equations (of arbitrary order) with singular coefficients.
We develop a very general operator-valued functional calculus for operators with an $H^{\infty}-$calculus. We then apply this to the joint functional calculus of two commuting sectorial operators when one has an $H^{\infty}$calculus. Using…
We describe some classes of linear operators on Banach spaces over non-Archimedean fields, which admit orthogonal spectral decompositions. Several examples are given.
We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…
In [2] we characterized in terms of a quadratic growth condition various metric regularity properties of the subdifferential of a lower semicontinuous convex function acting in a Hilbert space. Motivated by some recent results in [16] where…
We show that fractional powers of general sectorial operators on Banach spaces can be obtained by the harmonic extension approach. Moreover, for the corresponding second order ordinary differential equation with incomplete data describing…
If X is a sequentially complete locally convex space, then a quotient bounded operator T is regular (in the sense of Waelbroeck) if and only if it is a bounded element (in the sense of Allan) of the algebra of quotient bounded operators on…
In this paper we characterize multiplication operators induced by operator valued maps on Banach function spaces. We also study multiplication semigroups and stability of these operators.
We extend the De Giorgi--Nash--Moser theory to superposition operators of mixed fractional operators. In particular, we investigate several regularity properties for this class of operators. We establish the Caccioppoli-type inequality with…
Given an arbitrary $p$-Banach ideal $(0 < p \leq 1)$, we ask for geometrical properties of this ideal which are sufficient (and necessary) to allow a transfer of the principle of local reflexivity to this operator class.
We establish the weak Banach-Saks property for function spaces arising as the optimal domain of an operator.
This article studies regularity properties of multiplicative stochastic processes on infinite-dimensional Lie groups. We investigate conditions under which these processes admit c\`adl\`ag modifications and derive bounds on their local…
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…
The goal of this paper is to introduce and study some geometric properties of slice regular functions of quaternion variable like univalence, subordination, starlikeness, convexity and spirallikeness in the unit ball. We prove a number of…
We study the regularity of Fourier integral operators, by allowing their symbols to satisfy certain multi-parameter characteristics. As a result, we give an extension of Seeger-Sogge-Stein theorem on product spaces.
We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are…
In this paper, regularity properties of Cauchy problem for linear and nonlinear abstract Schr\"odinger equations in vector-valued function spaces are obtained.