Spectrum of class operators.
Spectrum of generators of a noncommutative Banach algebra
Spectrum of infinite block matrices and -triangular operators.
Spectrum preserving linear mappings in Banach algebras
Let A and B be two unitary Banach algebras. We study linear mappings from A into B which preserve the polynomially convex hull of the spectrum. In particular, we give conditions under which such surjective linear mappings are Jordan morphisms.
Spektrale Invarianz bei verallgemeinerten Eigenfunktionsentwicklungen.
Spektraltheorie linksdefiniter Differenzengleichungssysteme.
Spektraltheorie stetiger Endomorphismen eines lokal-konvexen Raumes.
Splines and pseudo-inverses
Square functions, bounded analytic semigroups, and applications
To any bounded analytic semigroup on Hilbert space or on -space, one may associate natural ’square functions’. In this survey paper, we review old and recent results on these square functions, as well as some extensions to various classes of Banach spaces, including noncommutative -spaces, Banach lattices, and their subspaces. We give some applications to functional calculus, similarity problems, multiplier theory, and control theory.
Squaring a reverse AM-GM inequality
Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ, Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B), and Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))², where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.
Stabilité et convergence dans les problèmes de perturbation singulière
Stability and spectra of C0-semigroups.
Stability of infinite ranges and kernels
Let A(·) be a regular function defined on a connected metric space G whose values are mutually commuting essentially Kato operators in a Banach space. Then the spaces and do not depend on z ∈ G. This generalizes results of B. Aupetit and J. Zemánek.
Stability of operator semigroups: ideas and results
Stability of the bases and frames reproducing kernels in model spaces
We study the bases and frames of reproducing kernels in the model subspaces of the Hardy class in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels under “small” perturbations of the points . We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.
Stability of the index of a linear relation under compact perturbations
We prove the stability under compact perturbations of the algebraic index of a Fredholm linear relation with closed range acting between normed spaces. Our main tool is a result concerning the stability of the index of a complex of Banach spaces under compact perturbations.
Stability of the local spectrum.
Stability of the method of least squares for finding the eigenvalues of a symmetric operator
Stability of the spectrum for transfer operators
Stability on coupling SIR epidemic models with vaccination.