Generic stability of the spectra for bounded linear operators on Banach spaces (Q1305819)

Let \(\mathbb{C}\) be the complex plane, \(K(\mathbb{C})\) be space of all nonempty compact subsets of \(\mathbb{C}\). If \(X\neq\{0\}\) denotes a complex Banach space, then \(B(X)\) is the Banach space of all bounded linear operators in \(X\) and \(\sigma(T)\) denotes the spectrum of \(T\). The main results of this article are: 1. \(\sigma:B(X)\to K(\mathbb{C})\) is an upper semicontinuous mapping. 2. The spectra of bounded linear operators are stable on a dense residual subset of \(B(X)\).