A new mode of convergence of linear operators in a Hilbert space (Q2301856)

A new concept of \(z\)-convergence of subspaces of a Hilbert space is introduced in the paper under review. Based on this notion, \(z\)-convergence of linear operators in a Hilbert space is defined, which generalizes the strong resolvent convergence of selfadjoint operators. Many basic properties of \(z\)-convergence are developed, among which it is proved that the set of selfadjoint operators is closed under \(z\)-convergence.