Related papers: Family index for Fredholm extensions of semi-Fredh…

This paper concerns Fredholm theory in several variables, and its applications to Hilbert spaces of analytic functions. One feature is the introduction of ideas from commutative algebra to operator theory. Specifically, we introduce a…

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…

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.

Based on operators borrowed from scattering theory, several concrete realizations of index theorems are proposed. The corresponding operators belong to some C*-algebras of pseudo-differential operators with coefficients which either have…

We construct a Hilbert scale on $L^2([0,1])$ via a unitary twist operator that maps the standard Fourier basis to half-integer frequency exponentials. The resulting weighted spaces, equipped with norms indexed by $(1+|k+\tfrac{1}{2}|^2)^s$,…

In this paper we consider A-Fredholm and semi-A-Fredholm operators on Hilbert C*-modules over a W*-algebra A defined in [3],[10]. Using the assumption that A is a W*-algebra (and not an arbitrary C*-algebra), we obtain several results such…

Let $A$ be a linear bounded operator in a Hilbert space $H$, $N(A)$ and $R(A)$ its null-space and range, and $A^*$ its adjoint. The operator $A$ is called Fredholm iff $dim N(A)= dim N(A^*):=n<\infty$ and $R(A)$ and $R(A^*)$ are closed…

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…

For bounded right linear operators, in a right quaternionic Hilbert space with a left multiplication defined on it, we study the approximate $S$-point spectrum. In the same Hilbert space, then we study the Fredholm operators and the…

In a previous paper we introduced the unitary conjugation groupoid associated to any unital separable Type I C*-algebra. This groupoid encodes the representation-theoretic structure of the algebra through the action of its unitary group on…

This paper is devoted to the space of unbounded Fredholm operators equipped with the graph topology, the subspace of operators with compact resolvent, and their subspaces consisting of self-adjoint operators. Our main results are the…

We extend the relative index theorem on non-compact manifolds to encompass a wide variety of hypoelliptic differential operators of arbitrary order, demonstrating that the change in index when changing a differential operator locally can be…

A classical problem in operator theory has been to determine the spectrum of Toeplitz-like operators on Hilbert spaces of vector-valued holomorphic functions on the open unit ball in C^m. In this note we obtain necessary conditions for…

In this paper, we define an analytical index for a continuous family of Fredholm operators parameterized by a topological space $\mathbb{X}$ into a Hilbert space $H,$ as a sequence of integers, extending naturally the usual definition of…

In 1970s Segal outlined proofs of two theorems relating spaces of Fredholm and self-adjoint Fredholm operators with Quillen's constructions used to define higher algebraic K-theory. In the present paper we provide detailed proofs of these…

In noncommutative geometry one is interested in invariants such as the Fredholm index or spectral flow and their calculation using cyclic cocycles. A variety of formulae have been established under side conditions called summability…

We prove that a first order linear differential operator G with unbounded operator coefficients is Fredholm on spaces of functions on the real line with values in a reflexive Banach space if and only if the corresponding strongly continuous…

In this paper we study the semi-Fredholm property of band-dominated operators $A$ and prove that it already implies the Fredholmness of $A$ in all cases where this is not disqualified by obvious reasons. Moreover, this observation is…

We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted L_p-Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions…

An algebraic analogue of the family of Fredholm operators is introduced for the family of row and column finite matrices, dubbed "Fredholm matrices." In addition, a measure is introduced which indicates how far a Fredholm matrix is from an…