A formula for gap between two closed operators
Let \(H_1\) and \(H_2\) are Hilbert spaces and \(A,B\in B(H_1,H_2)\). Then the gap between \(A\) and \(B\) is defined as the gap between the corresponding graphs \(G(A)\) and \(G(B)\), i.e., \( \theta(A,B)=\|P_{G(A)}-P_{G(B)}\|\). \textit{J.\,Faghih-Habibi} [Linear Algebra Appl.\ 186, 55--57 (1993; Zbl 0773.15011)] computed a formula for \(\theta(A,0)\), where \(A\) is an \(m\times n\) matrix. \textit{R.\,Nakamoto} [Math.\ Jap.\ 42, No.\,2, 219--232 (1995; Zbl 0842.47007)] generalized Habibi's formula for bounded operators \(A,B\in B(H_1,H_2)\). In the paper under review, the authors extend the results of these papers to the case of densely defined unbounded closed operators.
scientific article; zbMATH DE number 5702842
scientific article