Continuity of approximate point spectrum on the algebra \(B(X)\) (Q2851103)

Continuity is the core of many branches of mathematics. In this paper, the authors study some spectral properties using the continuity of the spectra viewed as multifunctions from \(B(X)\) into the complex plane (i.e, a point-to-set correspondence of \(B(X)\) into the complex plane). This is an interesting idea, from which the authors obtain some characterizations and some important properties, in particular, for the approximate point spectrum, the surjective spectrum and the spectrum of an operator.