Related papers: Rational dilation for operators associated with sp…
It is shown that rational dilation fails on broad collection of distinguished varieties associated to constrained subalgebras of the disk algebra of the form C + B A(D), where B is a finite Blaschke product with two or more zeros. This is…
Given a row contraction of operators on Hilbert space and a family of projections on the space which stabilize the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries which satisfy natural…
Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional…
This is a survey on discrete linear operators which, besides approximating in Jackson or near-best order, possess some interpolatory property at some nodes. Such operators can be useful in numerical analysis.
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general points. We prove a generalization of this to higher dimensional varieties, showing that smooth varieties of minimal degree can be interpolated…
Paul Halmos' work in dilation theory began with a question and its answer: Which operators on a Hilbert space can be extended to normal operators on a larger Hilbert space? The answer is interesting and subtle. The idea of representing…
Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
We give an alternative proof to Agler's famous result on success of rational dilation on an annulus by an application of a result due to Dritschel and McCullough. We show interplay between operators associated with an annulus, $C_{1,r}$ or…
We explore aspects of dilation theory in the finite dimensional case and show that for a commuting $n$-tuple of operators $T=(T_1,...,T_n) $ acting on some finite dimensional Hilbert space $H$ and a compact set $X\subset \mathbb{C}^n$ the…
Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, we explore a pure algebraic…
We consider interpolation inequalities for imbeddings of the $l^2$-sequence spaces over $d$-dimensional lattices into the $l^\infty_0$ spaces written as interpolation inequality between the $l^2$-norm of a sequence and its difference. A…
In this paper, we present more regularity conditions which ensure the boundedness of dilation operators on Besov and Triebel-Lizorkin spaces equiped with general weights.
In this paper, we define several types of maximal operators on sequence spaces occuring in Harmonic analysis and present various connections between them.
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
The aim of this paper is to characterize a fractal operator associated with multivariate fractal interpolation functions (FIFs) and study the several properties of this fractal operator. Further, with the help of this operator, we…
Let $\mathcal{H}$ be a complex Hilbert space and let $\big\{A_{n}\big\}_{n\geq 1}$ be a sequence of bounded linear operators on $\mathcal{H}$. Then a bounded operator $B$ on a Hilbert space $\mathcal{K} \supseteq \mathcal{H}$ is said to be…