Sur l'extension de normes sur des algèbres de matrices.
The convex analysis of unitarily invariant matrix functions.
The critical exponent of operators with constrained spectral radius
The Gerschgorin discs under unitary similarity
The intersection of the Gerschgorin regions over the unitary similarity orbit of a given matrix is studied. It reduces to the spectrum in some cases: for instance, if the matrix satisfies a quadratic equation, and also for matrices having "large" singular values or diagonal entries. This leads to a number of open questions.
The higher rank numerical range of nonnegative matrices
In this article the rank-k numerical range ∧k (A) of an entrywise nonnegative matrix A is investigated. Extending the notion of elements of maximum modulus in ∧k (A), we examine their location on the complex plane. Further, an application of this theory to ∧k (L(λ)) of a Perron polynomial L(λ) is elaborated via its companion matrix C L.
The norm of the product of a large matrix and a random vector.
The numerical Range of Matrix Polynomials
The optimal perturbation bounds for the weighted Moore-Penrose inverse.
The Perturbation Bounds for Eigenspaces of a Definite Matrix-Pair
The q-numerical range of tridiagonal matrices.
The spectral radii of an operator and its modulus
The Steinitz constant of the plane.
Toeplitz band matrices with exponentially growing condition numbers.
Transient behavior of powers and exponentials of large Toeplitz matrices.
Two applications of a bound on the Hadamard product with a Cauchy matrix.
Uniqueness of the operator attaining
Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices
Our motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices. Generalizing this result, we give a complete description of unitary similarity automorphisms of the space of Toeplitz-plus-Hankel matrices.
Universal bounds for matrix semigroups
We show that any compact semigroup of n × n matrices is similar to a semigroup bounded by √n. We give examples to show that this bound is best possible and consider the effect of the minimal rank of matrices in the semigroup on this bound.
Upper bounds for the best normal approximation.
Young's inequality in compact operators. The case of equality.