Tauberian operators in -adic analysis.
Tauberian operators on spaces of integrable functions.
Tensor products and elementary operators.
The Atkinson theorem in Hilbert -modules over -algebras of compact operators.
The C*-Algebra of the N-Dimensional Harmonic Oscillator.
The coincidence index for fundamentally contractible multivalued maps with nonconvex values
We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given.
The geometry of Kato Grassmannians
We discuss Fredholm pairs of subspaces and associated Grassmannians in a Hilbert space. Relations between several existing definitions of Fredholm pairs are established as well as some basic geometric properties of the Kato Grassmannian. It is also shown that the so-called restricted Grassmannian can be endowed with a natural Fredholm structure making it into a Fredholm Hilbert manifold.
The index for Fredholm elements in a Banach algebra via a trace
We show that the existence of a trace on an ideal in a Banach algebra provides an elegant way to develop the abstract index theory of Fredholm elements in the algebra. We prove some results on the problem of the equality of the nonzero exponential spectra of elements ab and ba and use the index theory to formulate a condition guaranteeing this equality in a quotient algebra.
The index for Fredholm elements in a Banach algebra via a trace II
We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity with the Jacobson property. The Weyl spectrum is then characterized in terms of the index.
The index of signature operators on Lipschitz manifolds
The Kato-type spectrum and local spectral theory
Let be a bounded operator on a complex Banach space . If is an open subset of the complex plane such that is of Kato-type for each , then the induced mapping has closed range in the Fréchet space of analytic -valued functions on . Since semi-Fredholm operators are of Kato-type, this generalizes a result of Eschmeier on Fredholm operators and leads to a sharper estimate of Nagy’s spectral residuum of . Our proof is elementary; in particular, we avoid the sheaf model of Eschmeier and...
The semigroup of Fredholm operators.
The spectral mapping theorem for the essential approximate point spectrum
The Stability of the Euler Characteristic for Hilbert Complexes.
The stability radius of a bundle of closed linear operators
Théorie de l'indice pour des opérateurs non-Fredholm
Toeplitz Operators with Frequency Modulated Semi-Almost Periodic Symbols.
Topological properties of nonlinear evolution equations
Two geometric constants for operators acting on a separable Banach space.
The main result of this paper is the following: A separable Banach space X is reflexive if and only if the infimum of the Gelfand numbers of any bounded linear operator defined on X can be computed by means of just one sequence on nested, closed, finite codimensional subspaces with null intersection.