Related papers: Drazin invertibility of linear operators on quater…
For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
The paper is devoted to obtaining conditions for the roughness of dichotomy in the Banach spaces. Deep analysis of the well known papers was considered. The main results also works for the case of unbounded operators.
We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.
In this paper, we investigate the invertibility of $I_Y+\delta TT^+$ when $T$ is a closed operator from $X$ to $Y$ with a generalized inverse $T^+$ and $\delta T$ is a linear operator whose domain contains $D(T)$ and range is contained in…
In this paper, we concern the kernel of linear operator for a class of Grushin equation. First, we study the kernel space of linear operator for a general Grushin equation. Then, we provide an exact expression for the kernel space of linear…
Let $A$ and $B$ be unital Banach algebras with $A$ a subalgebra of $B$. Denote the algebra of all $n\times n$ matrices with entries from $A$ by $M_{n}(A)$. In this paper we prove some results concerning the open question: If $A$ is inverse…
We prove that reiteratively hypercyclic operators have perfect spectrum. Consequently, it follows that there exist separable infinite dimensional Banach spaces that do not support any reiteratively hypercyclic operator. For this, we study…
Invertibility of Toeplitz operators on the Bergman space and the related Douglas problem are long standing open problems. In this paper we study the invertibility problem under the novel geometric condition on the image of the symbols,…
In this paper, we prove the boundedness of multilinear fractional integral operators from products of Hardy spaces associated with ball quasi-Banach function spaces into their corresponding ball quasi-Banach function spaces. As…
Arbitrary operator A on a Banach space X which is the generator of C_0-group with certain growth condition at infinity is considered. The relationship between its exponential type entire vectors and its spectral subspaces is found. Inverse…
In this paper we prove a local surjection theorem with continuous right-inverse for maps between Banach spaces, and we apply it to a class of inversion problems with loss of derivatives.
Even linear operators on infinite-dimensional spaces can display interesting dynamical properties and yield important links among functional analysis, differential and global geometry and dynamical systems, with a wide range of…
This paper deals with study of Birkhoff-James orthogonality of a linear operator to a subspace of operators defined between arbitrary Banach spaces. In case the domain space is reflexive and the subspace is finite dimensional we obtain a…
We show that there is an operator space notion of Lipschitz embeddability between operator spaces which is strictly weaker than its linear counterpart but which is still strong enough to impose linear restrictions on operator space…
This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We…
Motivated by a variety of representations of fractional powers of operators, we develop the theory of abstract Besov spaces $B^{ s, A }_{ q, X }$ for non-negative operators $A$ on Banach spaces $X$ with a full range of indices $s \in…
The problem of applying Nash-Moser Newton methods to obtain periodic solutions of the compressible Euler equations has led authors to identify the main obstacle, namely, how to invert operators which impose periodicity when they are based…
We give conditions for local diagonalization of an analytic operator family to a diagonal operator polynomial. The families are acting between real or complex Banach spaces. The basic assumption is given by stabilization of the Jordan…
Let $\Gamma$ be an oriented Jordan smooth curve and $\alpha$ be a diffeomorphism of $\Gamma$ onto itself which has an arbitrary nonempty set of periodic points. We prove criteria for one-sided invertiblity of the binomial functional…