相关论文: Remarks on $B(H)\otimes B(H)$
Boundedness properties for pseudodifferential operators with symbols in the bilinear H\"ormander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces and, in some cases, end-point…
The theorem like Pontryagin's maximum principle for multiple integrals is proved. Unlike the usual maximum principle, the maximum should be taken not over all matrices, but only on matrices of rank one. Examples are given.
Abstract approaches to maximum and anti-maximum principles for differential operators typically rely on the condition that all vectors in the domain of the operator are dominated by the leading eigenfunction of the operator. We study the…
We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we estimate lower bounds of…
We provide some new estimates for distances in harmonic function spaces of several variables related to mixed norm spaces.Some of them extend previously known assertions in this direction in the unit ball and upperhalfspace.
We investigate the interplay among three key properties of bounded linear operators between Banach spaces: the Bhatia-\v{S}emrl property, strong subdifferentiability and the condition that the essential norm is strictly less than the…
We obtain new inequalities involving Berezin norm and Berezin number of bounded linear operators defined on a reproducing kernel Hilbert space $\mathscr{H}.$ Among many inequalities obtained here, it is shown that if $A$ is a positive…
This paper presents a solution to a problem from superanalysis about the existence of Hilbert-Banach superalgebras. Two main results are derived: 1) There exist Hilbert norms on some graded algebras (infinite-dimensional superalgebras…
It is shown that the formula for the M\"obius pseudodistance for the annulus yields better estimates than previously known for the constant in the Bergman space maximum principle. A maximum principle for the Fock space is proved.
We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…
Let $A,B\in B(H)$. We present among others a simple proof of the widely known result stating that if $0\leq A\leq B$, then $\sqrt A\leq \sqrt B$. The same idea is used to prove that if $0\leq A\leq B$ and $A$ is invertible, then $B$ too is…
This paper investigates the boundedness of bilinear pseudo-differential operators with symbols in the H\"{o}rmander class $BS_{\varrho,\delta}^m(\mathbb{R}^n)$ in the previously unexplored regime $0 \leq \varrho < \delta < 1$. We establish…
We introduce a numerical radius operator space $(X, \mathcal{W}_n)$. The conditions to be a numerical radius operator space are weaker than the Ruan's axiom for an operator space $(X, \mathcal{O}_n)$. Let $w(\cdot)$ be the numerical radius…
We give necessary and sufficient conditions for two weight norm inequalities for Haar multipliers operators and for square functions. We also give sufficient conditions for two weight norm inequalities for the Hilbert transform.
In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove \begin{align*} \|f(A)Xg(B)\pm…
We give a new proof for an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools from matrix theory, (analytic) optimization theory and…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…
Recently, the quantum brachistochrone problem is discussed in the literature by using non-Hermitian Hamilton operators of different type. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the…
Inequalities for product operators on mixed norm Lebesgue spaces and permuted mixed norm Lebesgue spaces are established. They depend only on inequalities for the factors and on the Lebesgue indices involved. Inequalities for the bivariate…