Related papers: Operator inequalities dealing with operator equati…
Resolvent compositions were recently introduced as monotonicity-preserving operations that combine a set-valued monotone operator and a bounded linear operator. They generalize in particular the notion of a resolvent average. We analyze the…
In various contexts in mathematical physics one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the…
We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.
The kinetic energy operator of a quantum particle with position dependent mass and the associated ordering ambiguity is revisited. We introduce a new form of this operator which is a continues or discreet superposition of the acceptable…
Let $\mathcal{B}(\mathcal{H})$ be the algebra of all bounded linear operators on a complex Hilbert space $\mathcal{H}$. In this paper, we first establish several sharp improved and refined versions of the Bohr's inequality for the functions…
In this paper we investigate a notion of relative operator entropy, which develops the theory started by J.I. Fujii and E. Kamei [Math. Japonica 34 (1989), 341--348]. For two finite sequences $\mathbf{A}=(A_1,...,A_n)$ and…
We consider the numerical solution of the equation - \Delta u - f(u) = g, for the unknown u satisfying Dirichlet conditions in a bounded domain. The nonlinearity f has bounded, continuous derivative. The algorithm uses the finite element…
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the…
We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
In this paper we present some key moments in the history of Morita equivalence for operator algebras.
We review recent results on functional inequalities for systems of orthonormal functions. The key finding is that for various operators the orthonormality leads to a gain over a simple application of the triangle inequality. The operators…
In this note, we study the complex constant rank condition for differential operators and its implications for coercive differential inequalities. These are inequalities of the form \[ \Vert A u \Vert_{L^p} \leq \Vert \mathscr{A} u…
In this paper the complete solution of the restricted inequalities for supremal operators are given. The boundedness of the composition of supremal operators with the Hardy and Copson operators in weighted Lebesgue spaces are characterized.
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
We give a construction of impurity operators in the `algebraic analysis' picture of RSOS models. Physically, these operators are half-infinite insertions of certain fusion-RSOS Boltzmann weights. They are the face analogue of insertions of…
We study infinite order differential operators acting in the spaces of exponential type entire functions. We derive conditions under which such operators preserve the set of Laguerre entire functions which consists of the polynomials…
This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and…
In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…
We review the theory of first BGG operators and study how to approach them and find their solution on homogeneous geometries. We provide many new examples of parabolic geometries that admit solutions of first BGG operators with many…