Related papers: Some basic properties of block operator matrices
We use the method of monotone iterations to obtain fixed point and coupled fixed point results for mixed monotone operators in the setting of partially ordered sets, with no additional assumptions on the partial order and with no…
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…
In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. \ We first establish a criterion on the coprime-ness of two singular inner functions and…
In this article we consider 2-dimensional surfaces. We define some new operators which enable us to evaluate quantities of the surface, such invariants, in a more systematic way.
A recent development in random matrix theory, the intrinsic freeness principle, establishes that the spectrum of very general random matrices behaves as that of an associated free operator. This reduces the study of such random matrices to…
We relate dual-band general Toeplitz operators to block truncated Toeplitz operators and, via equivalence after extension, with Toeplitz operators with $4 \times 4$ matrix symbols. We discuss their norm, their kernel, Fredhomlness,…
Let $\mathbb{A}=\left( \begin{array}{cc} A & 0 \\ 0 & A \\ \end{array} \right)$ be the $2\times2$ diagonal operator matrix determined by a positive bounded operator $A$. For semi-Hilbertian operators $X$ and $Y$, we first show that…
In the first part of this paper we give an elementary proof of the fact that if an infinite matrix $A$, which is invertible as a bounded operator on $\ell^2$, can be uniformly approximated by banded matrices then so can the inverse of $A$.…
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 introduce a set of block factor-width-two matrices, which is a generalisation of factor-width-two matrices and is a subset of positive semidefinite matrices. The set of block factor-width-two matrices is a proper cone and…
We investigate two types of boundedness criteria for bilinear Fourier multiplier operators with symbols with bounded partial derivatives of all (or sufficiently many) orders. Theorems of the first type explicitly prescribe only a certain…
We introduce unbounded multipliers on operator spaces. These multipliers generalize both, regular operators on Hilbert C*-modules and (bounded) multipliers on operator spaces.
In this paper we study the stability properties of strongly continuous semigroups generated by block operator matrices. We consider triangular and full operator matrices whose diagonal operator blocks generate polynomially stable…
The concept of operator frame can be considered as a generalization of frame. Firstly, we introduce the notion of operator frame for the set of all adjointable operators $Hom_{\mathcal{A}}^{\ast}(\mathcal{X})$ on a Hilbert…
We propose two interrelated advances in the theory of adjointable operators on Hilbert C*-modules. First, we give a set of equivalent, verifiable conditions characterizing positivity of general $n\times n$ block operator matrices acting on…
Bidiagonal matrices are widespread in numerical linear algebra, not least because of their use in the standard algorithm for computing the singular value decomposition and their appearance as LU factors of tridiagonal matrices. We show that…
The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its…
For bilinear Fourier multipliers that contain some oscillatory factors, boundedness of the operators between Lebesgue spaces is given including endpoint cases. Sharpness of the result is also considered.
It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. We give a new algorithm by evaluation and interpolation which is faster than…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…