In most classical Banach spaces of holomorphic functions on the unit disk in which polynomials are dense, the Abel means (also called the dilates) $f_r (z) := f(rz)$ of a function $f$ converge in the norm of the space to the original function $f$. In 2016, O. El-Fallah, E. Fricain, K. Kellay, J. Mashreghi, and T. Ransford showed that there are a non extreme point $b$ in $H^\infty$ and a function $f$ in the respective de Branges-Rovnyak space $\mathcal{H} (b)$ such that $f_r$ diverges to $+\infty$ in the $\mathcal{H} (b)$-norm. In this talk, I will show an improvement of the previous result: there exist a non extreme point $b$ in $H^\infty$ and a function $f$ in $\mathcal{H} (b)$ such that the logarithmic means $L_r(f)$ diverges to $+\infty$ in the $\mathcal{H} (b)$-norm. I will also present an abstract result in summability theory in Banach spaces and show some of its consequences on the summability of the Taylor expansion of functions in de Branges-Rovnyak spaces. Joint work with Javad Mashreghi and Thomas Ransford.