Characterizations of Moore-Penrose inverses of closed linear relations
in Hilbert spaces
Characterizations of Moore-Penrose inverses of closed linear relations
in Hilbert spaces
This paper examines the Moore-Penrose inverses of closed linear relations in Hilbert spaces and establishes the result $\rho(\mathcal{A}) = \{\lambda \in \mathbb{C}: \lambda^{2} \in \rho(TT^{\dagger}) \cap \rho(T^{\dagger}T)\}$, where $\mathcal{A} = \begin{bmatrix} 0 & T^{\dagger} T & 0 \end{bmatrix}$, with $T$ being a closed and bounded linear relation from a Hilbert …