Noyaux absolument mesurables ou basiques et opérateurs nucléaires
Noyaux associés à des opérateurs de Faraut
n-supercyclic operators
We show that there are linear operators on Hilbert space that have n-dimensional subspaces with dense orbit, but no (n-1)-dimensional subspaces with dense orbit. This leads to a new class of operators, called the n-supercyclic operators. We show that many cohyponormal operators are n-supercyclic. Furthermore, we prove that for an n-supercyclic operator, there are n circles centered at the origin such that every component of the spectrum must intersect one of these circles.
N-th roots of a non-negative operator: conditions for uniqueness.
Nuclear spaces of maximal diametral dimension
Numerical Algorithms for the Nevanlinna-Pick Problem.
Numerical index of vector-valued function spaces
We show that the numerical index of a -, -, or -sum of Banach spaces is the infimum of the numerical indices of the summands. Moreover, we prove that the spaces C(K,X) and (K any compact Hausdorff space, μ any positive measure) have the same numerical index as the Banach space X. We also observe that these spaces have the so-called Daugavet property whenever X has the Daugavet property.
Numerical radius and operator norm inequalities.
Numerical radius inequalities for 2 × 2 operator matrices
We derive several numerical radius inequalities for 2 × 2 operator matrices. Numerical radius inequalities for sums and products of operators are given. Applications of our inequalities are also provided.
Numerical radius inequalities for Hilbert space operators
It is shown that if A is a bounded linear operator on a complex Hilbert space, then 1/4 ||A*A + AA*|| ≤ (w(A))² ≤ 1/2 ||A*A + AA*||, where w(·) and ||·|| are the numerical radius and the usual operator norm, respectively. These inequalities lead to a considerable improvement of the well known inequalities 1/2 ||A|| ≤ w(A) ≤ || A||. Numerical radius inequalities for products and commutators of operators are also obtained.
Numerical radius inequalities for Hilbert space operators. II
We give several sharp inequalities involving powers of the numerical radii and the usual operator norms of Hilbert space operators. These inequalities, which are based on some classical convexity inequalities for nonnegative real numbers and some operator inequalities, generalize earlier numerical radius inequalities.
Numerical range of operators acting on Banach spaces
The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small...
Numerical ranges of some composition operators.
This paper is a short survey on the numerical range of some composition operators. The first part is devoted to composition operators on the Hilbert Hardy space H2 on the unit disk. The results are due to P. Bourdon, J. Shapiro and V. Matache.In the second part we study the numerical range of composition operators on the Hilbert space H2 of Dirichlet series. These results are due to H. Queffélec and the author.The third part is devoted to compactness connected with fixed points in the setting of...