Related papers: Gateaux derivative of matrix norms in operator spa…
This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear…
We study the duals of a certain class of finite-dimensional operator systems, namely the class of operator systems associated to tolerance relations on finite sets or equivalently the class of operator systems that are associated with…
A Moutard type transformation for matrix generalized analytic functions is derived. Relations between Moutard type transforms and gauge transformations are demonstrated.
We study the probability assignment for the outcomes of time-extended measurements. We construct the class-operator that incorporates the information about a generic time-smeared quantity. These class-operators are employed for the…
Several subadditivity results and conjectures are given for matrices (or operators), block-matrices, concave functions and norms.
It is shown that the matrix KP hierarchy can yield new integrable equations in $(2+1)$-dimensions along with the corresponding Lax pair. For particular gauge choice this may result derivative and also a higher order nonlinear extension of…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We extend the $\lambda$-theory of operator spaces given by Defant and Wiesner (2014), that generalizes the notion of the projective, Haagerup and Schur tensor norm for operator spaces to matrix ordered spaces and Banach $*$-algebras. Given…
In this paper we estimate the norm of operator acting from one Bilateral Grand Lebesgue Space (BGLS) into other Bilateral Grand Lebesgue Space. We also give some examples to show the sharpness of offered inequalities.
We investigate $\rho$-orthogonality and its local symmetry in the space of bounded linear operators. A characterization of Hilbert space operators with symmetric numerical range is established in terms of $\rho$-orthogonality. Further, we…
Consider the $n!$ different unitary matrices that permute $n$ $d$-dimensional quantum systems. If $d\geq n$ then they are linearly independent. This paper discusses a sense in which they are approximately orthogonal (with respect to the…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
In this paper we characterize the Birkhoff--James orthogonality with respect to the numerical radius norm $v(\cdot)$ in $C^*$-algebras. More precisely, for two elements $a, b$ in a $C^*$-algebra $\mathfrak{A}$, we show that $a\perp_{B}^{v}…
In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a…
Subaddivity type matrix inequalities for concave funcions and symetric norms are given.
Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…
In this paper, the formal derivative operator defined with respect to context-free grammars is used to prove some properties about binomial coefficients and multifactorial numbers. In addition, we extend the formal derivative operator to…
We prove a general theorem establishing the bispectrality of noncommutative Darboux transformations. It has a wide range of applications that establish bispectrality of such transformations for differential, difference and q-difference…
Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations - matrices - acting on the data are often not accessible directly…
We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…