Related papers: Operator capacity, the Brascamp--Lieb inequality a…
In this paper we consider a generalized version of bounded oscillation operators, involving new parameters in the definition, as well as considering the operators on vector-valued function spaces. With this definition we will capture some…
In this note we give simple proofs of several results involving maximal truncated Calde\'on-Zygmund operators in the general setting of rearrangement invariant quasi-Banach function spaces by sparse domination. Our techniques allow us to…
The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…
Continuing the study initiated in our earlier article [7], this paper aims to characterize various continuity properties of nonlinear composition operators acting on some sequence spaces, giving special attention to the space of sequences…
Very recently, motivated by the result of Bhatia and \v{S}emrl which characterizes the Birkhoff-James orthogonality of operators on a finite dimensional Hilbert space in terms of norm attaining points, the Bhatia-\v{S}emrl property was…
We develop a new functional-analytic technique for investigating the degree of noncompactness of an operator defined on a quasinormed space and taking values in a Marcinkiewicz space. The main result is a general principle from which it can…
We characterize proximity operators, that is to say functions that map a vector to a solution of a penalized least squares optimization problem. Proximity operators of convex penalties have been widely studied and fully characterized by…
We develop an operator-theoretic framework for stability and statistical concentration in nonlinear inverse problems with block-structured parameters. Under a unified set of assumptions combining blockwise Lipschitz geometry, local…
We study uniform $\epsilon-$BPB approximations of bounded linear operators between Banach spaces from a geometric perspective. We show that for sufficiently small positive values of $\epsilon,$ many geometric properties like smoothness,…
The purpose of this paper is to systematically study compactness and essential norm properties of operators on a very general class of weighted Fock spaces over $\C$. In particular, we obtain rather strong necessary and sufficient…
Through refined asymptotic analysis based on the normal approximation, we study how higher-order coding performance depends on the mean power as well as on finer statistics of the input power. We introduce a multifaceted power model in…
In this paper we develop a general theoretical tool for the establishment of the boundedness of notoriously difficult operators (such as potentials) on certain specific types of rearrangement-invariant function spaces from analogous…
This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-adjoint operator. A necessary condition is that the domain of…
The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand…
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible…
Similar to the theory of finite Markov chains it is shown that in a Banach space $X$ ordered by a closed cone $K$ with nonempty interior int($K$) a power bounded positive operator $A$ with compact power such that its trajectories for…
We formulate generalized Brascamp-Lieb inequalities for representations of bipartite quivers and establish necessary and sufficient conditions for such inequalities. Notably, we show contra Lieb that Gaussians do not saturate certain types…
We prove number of quantitative stability bounds for the cases of equality in Petz's monotonicity theorem for quasi-relative entropies defined in terms of an operator monotone decreasing functions. Included in our results is a bound in…
We introduce quotient maps in the category of operator systems and show that the maximal tensor product is projective with respect to them. Whereas, the maximal tensor product is not injective, which makes the $({\rm el},\max)-nuclearity…
We show that a densely defined closable operator $A$ such that the resolvent set of $A^2$ is not empty is necessarily closed. This result is then extended to the case of a polynomial $p(A)$. We also generalize a recent result by…