The Horn Conjecture for Sums of Compact Selfadjoint Operators

Error bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion

On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Spectral inequalities for non-selfadjoint elliptic operators and application to the null-controllability of parabolic systems

We consider elliptic operators A on a bounded domain, that are compact perturbations of a selfadjoint operator. We first recall some spectral properties of such operators: localization of the spectrum and resolvent estimates. We then derive a spectral inequality that measures the norm of finite sums of root vectors of A through an observation, with an exponential cost. Following the strategy of...

$L^p$-Conjecture on Hypergroups

In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions  for a weighted Lebesgue space  $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$.  Among the other things, we also show that if $K$ is a locally compact hyper...

A new topology on the space of unbounded selfadjoint operators and the spectral flow

We define a new topology, weaker than the gap topology, on the space of selfadjoint unbounded operators on a separable Hilbert space. We show that the subspace of selfadjoint Fredholm operators represents the functor K from the category of compact spaces to the category of abelian groups and prove a similar result for K. We define the spectral flow of a continuous path of selfadjoint Fredholm o...