相关论文: Topological categories related to Fredholm operato…

We review an approach to the index theory of operator algebras associated with Lie groups of quantized canonical transformations. Main points are an ellipticity condition ensuring the Fredholm property, the definition of localized algebraic…

This paper provides a $K$-theoretic obstruction for higher kernel dimension for Dirac operators. For this we use a fibre-wise Dirac operator that gives rise to a family of Fredholm operators representing a class in topological $K$-theory.…

In the paper one considers the local structure of the Fredholm joint spectrum of commuting $n$-tuples of operators. A connection between the spatial characteristics of operators and the algebraic invariant of the corresponding coherent…

The index of a pseudo B-Fredholm operator will be defined and generalize the usual index of a B-Fredholm operator. This concept will be used to extend some known results in Fredholm's theory. Among other results, the nullity, the…

We consider the mapping properties of generalized Laplace-type operators ${\mathcal L} = \nabla^* \nabla + {\mathcal R}$ on the class of quasi-asymptotically conical (QAC) spaces, which provide a Riemannian generalization of the QALE…

Given C*-algebras A and B and an imprimitivity A-B-bimodule X, we construct an explicit isomorphism X_* : K_i(A) --> K_i(B) where K_i denote the complex K-theory functors for i=0, 1. Our techniques do not require separability nor existence…

we show that the definitions of some classes of semi-Fredholm operators, which use the language of algebra and first introduced by X. Fang in [8], are equivalent to that of some well-known operator classes. For example, the concept of…

Equivariant twisted K theory classes on compact Lie groups $G$ can be realized as families of Fredholm operators acting in a tensor product of a fermionic Fock space and a representation space of a central extension of the loop algebra $LG$…

This paper presents the Fredholm theory on l^p-spaces for band-dominated operators and important subclasses, such as operators in the Wiener algebra. It particularly closes several gaps in the previously known results for the case p=\infty…

We study the Fredholm properties of a general class of elliptic differential operators on $\R^n$. These results are expressed in terms of a class of weighted function spaces, which can be locally modeled on a wide variety of standard…

Using the general formalism of [12], a study of index theory for non-Fredholm operators was initiated in [9]. Natural examples arise from $(1+1)$-dimensional differential operators using the model operator $D_A$ in $L^2(\mathbb{R}^2; dt…

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…

Kasparov $KK$-groups $KK(A,B)$ are represented as homotopy groups of the Pedersen-Weibel nonconnective algebraic $K$-theory spectrum of the additive category of Fredholm $(A,B)$-bimodules for $A$ and $B$, respectively, a separable and…

Twisted K-theory classes over compact Lie groups can be realized as families of Fredholm operators using the representation theory of loop groups. In this talk I want to show how to deform the Fredholm family, in the sense of quantum…

The quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which…

A bounded operator $T$ on a separable, complex Hilbert space is said to be odd symmetric if $I^*T^tI=T$ where $I$ is a real unitary satisfying $I^2=-1$ and $T^t$ denotes the transpose of $T$. It is proved that such an operator can always be…

Given a Lie group $G$ of quantized canonical transformations acting on the space $L^2(M)$ over a closed manifold $M$, we define an algebra of so-called $G$-operators on $L^2(M)$. We show that to $G$-operators we can associate symbols in…

The Fredholm property of Toeplitz operators on the $p$-Fock spaces $F_\alpha^p$ on $\mathbb{C}^n$ is studied. A general Fredholm criterion for arbitrary operators from the Toeplitz algebra $\mathcal{T}_{p,\alpha}$ on $F_\alpha^p$ in terms…

This is an expository article. It discusses an approach to hypoelliptic Fredholm index theory based on noncommutative methods (groupoids, C*-algebras, K-theory). The paper starts with an explicit index theorem for scalar second order…

This note is an expository contribution for a proceedings volume of the workshop "Higher Segal Spaces and their Applications to Algebraic K-theory, Hall Algebras, and Combinatorics". We survey various versions of Waldhausen's S-construction…