Related papers: The index bundle for Fredholm morphisms
In this paper, we define an analytical index for continuous families of Fredholm operators parameterized by a topological space $\mathbb{X}$ into a Banach space $X.$ We also consider the Weyl spectrum for continuous families of bounded…
We provide a thorough construction of a system of compatible determinant line bundles over spaces of Fredholm operators, fully verify that this system satisfies a number of important properties, and include explicit formulas for all…
We consider special classes of linear bounded operators in Banach spaces and suggest certain operator variant of symbolic calculus. It permits to formulate an index theorem and to describe Fredholm properties of elliptic pseudo-differential…
In this paper, we established Fredholm theory of the linearized ${{\bar \partial}}$-operator and studied the additivity of its index.
In this paper, we define and index for continuous families of semi-Fredholm bounded liner operators. Moreover, we study various regularities and semiregularities of continuous families of bounded linear operators.
This paper is devoted to Fredholm realizations of semi-Fredholm operators in a Hilbert space. Such a realization is determined by an abstract boundary condition, which is a subspace of the space of abstract boundary values. We find the…
In this work it is introduced the notion of regular Fredholm pair, i.e. a Fredholm pair whose operators are regular. The main properties of these objects are studied, and what is more, they are entirely classified. Furthermore, the index of…
This paper is a continuation of the paper (A.G.Ramm, Amer. Math. Monthly, 108, N 9, (2001), 855-860), where bounded Fredholm operators are studied. The theory of bounded linear Fredholm-type operators is presented in many texts. This paper…
The index of a selfadjoint Fredholm operator is zero by the well-known fact that the kernel of a selfadjoint operator is perpendicular to its range. The Fredholm index was generalised to families by Atiyah and J\"anich in the sixties, and…
While in \cite{HB} we studied classes of Fredholm-type operators defined by the homomorphism $\Pi$ from $L(X)$ onto the Calkin algebra $\mathcal{C}(X)$, $X$ being a Banach space, we study in this paper two classes of Fredholm-type operators…
Naively, the analytic index of a family of self-adjoint Fredholm operators ought to be (an equivalence class of) the family of the kernels of these operators. The present paper is devoted to a rigorous version of this idea based on ideas of…
We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles over smooth manifolds with respect to groups of authomorphisms.
We consider bisingular pseudodifferential operators which are pseudodifferential operators of tensor product type. These operators are defined on the product manifold $M_1 \times M_2$, for closed manifolds $M_1$ and $M_2$. We prove a…
We compute the equivariant cohomology Chern character of the index of elliptic operators along the leaves of the foliation of a flat bundle. The proof is based on the study of certain algebras of pseudodifferential operators and uses…
We consider Toeplitz and Hankel operators with piecewise continuous generating functions on $l^p$-spaces and the Banach algebra generated by them. The goal of this paper is to provide a transparent symbol calculus for the Fredholm property…
We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. For this, we give few results on diffeological principal bundles with (a priori) no local…
This article provides a version of scale calculus geared towards a notion of (nonlinear) Fredholm maps between certain types of Frechet spaces, retaining as many as possible of the properties Fredholm maps between Banach spaces enjoy, and…
We characterize the groupoids for which an operator is Fredholm if, and only if, its principal symbol and all its boundary restrictions are invertible. A groupoid with this property is called {\em Fredholm}. Using results on the Effros-Hahn…
Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals.
Dirac-Schr\"{o}dinger systems play a central role when modeling Dirac bundles and Dirac-Schr\"{o}dinger operators near the boundary, along ends or near other singularities of Riemannian manifolds. In this article we develop the Fredholm…