International Seminar Series on Advances in Operator Theory and Inequalities #2

The talk is based on Dirichlet-type spaces on the unit bidisc. We shall begin with a notion of Dirichlet-type spaces $\mathcal{D}(\mu_1, \mu_2)$ on the unit bidisc $\mathbb{D}^2$ with harmonic weights corresponding to finite positive Borel measures $\mu_1$ and $\mu_2$ supported on the unit circle. Then we show that the coordinate functions $z_1$ and $z_2$ are multipliers for...

We study the approximate minimizing property (AMp) for operators, a localized Bishop-Phelps-Bollob\'{a}s type property with respect to minimum norm. Given Banach spaces $X$ and $Y$ we define a new class $\mathcal{AM}(X,Y)$ of bounded linear operators from $X$ to $Y$ for which the pair $(X,Y)$ satisfies the AMp. We provide a necessary and sufficient condition for non-injective operators from...