An irreducible semigroup of idempotents
We construct a semigroup of bounded idempotents with no nontrivial invariant closed subspace. This answers a question which was open for some time.
An Iteration Method for Studying the Bifurcation of Solutions of the Nonlinear Equations, L(...) u + ..R (..., u) = 0 .
An iterative approach to a constrained least squares problem.
An -functional calculus for power-bounded operators on certain UMD spaces
For 1 ≤ q < ∞, let denote the Banach algebra consisting of the bounded complex-valued functions on the unit circle having uniformly bounded q-variation on the dyadic arcs. We describe a broad class ℐ of UMD spaces such that whenever X ∈ ℐ, the sequence space ℓ²(ℤ,X) admits the classes as Fourier multipliers, for an appropriate range of values of q > 1 (the range of q depending on X). This multiplier result expands the vector-valued Marcinkiewicz Multiplier Theorem in the direction q >...
An operator inequality.
An Operator Inequality.
An operator on a separable Hilbert space with all polynomials hypercyclic
An operator on a separable Hilbert space with many hypercyclic vectors
An operator-theoretic approach to theorems of the Pick-Nevanlinna and carathéodory types.
An operator-theoretic approach to truncated moment problems
We survey recent developments in operator theory and moment problems, beginning with the study of quadratic hyponormality for unilateral weighted shifts, its connections with truncated Hamburger, Stieltjes, Hausdorff and Toeplitz moment problems, and the subsequent proof that polynomially hyponormal operators need not be subnormal. We present a general elementary approach to truncated moment problems in one or several real or complex variables, based on matrix positivity and extension. Together...
An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales.
An overview of some recent developments on the Invariant Subspace Problem
This paper presents an account of some recent approaches to the Invariant Subspace Problem. It contains a brief historical account of the problem, and some more detailed discussions of specific topics, namely, universal operators, the Bishop operators, and Read’s Banach space counter-example involving a finitely strictly singular operator.
An upper bound for the local time-decay of scattering solutions for the Schrödinger equation with Coulomb potential
Analyse spectrale des formes automorphes et séries d'Eisenstein.
Analytic families of semigroups.
Analytic formulae for determinant systems in Banach spaces
Analytic formulas for the hyperbolic distance between two contractions
In this paper we give some analytic formulas for the hyperbolic (Harnack) distance between two contractions which permit concrete computations in several situations, including the finite-dimensional case. The main consequence of these formulas is the proof of the Schwarz-Pick Lemma. It modifies those given in [13] by the avoidance of a general Schur type formula for contractive analytic functions, more exactly by reducing the case to the more manageable situation when the function takes as values...
Analytic Functions of Topological Proper Contractions.
Analytic functions on c0.
Analytic joint spectral radius in a solvable Lie algebra of operators
We introduce the concept of analytic spectral radius for a family of operators indexed by some finite measure space. This spectral radius is compared with the algebraic and geometric spectral radii when the operators belong to some finite-dimensional solvable Lie algebra. We describe several situations when the three spectral radii coincide. These results extend well known facts concerning commuting n-tuples of operators.