Domination conditions and spectral multiplicity of operators
Let \(X\) be a Banach space, \(A: X \to X\) be a bounded linear operator. The quantity \(\mu(A) = \inf\{ \dim E: \text{span}\{A^nE \}_{n=0}^\infty = X\}\) is called the spectral multiplicity of \(A\). For a direct sum of operators, the following inequalities are known: \(\max\{\mu(A), \mu(B)\} \leq \mu(A \oplus B) \leq \mu(A) + \mu(B)\). In the paper under review, developing technique from \textit{M. T. Karaev} [Arch. Math. 93, No. 2, 147--152 (2009; Zbl 1189.46041)], the author studies conditions under which \(\mu(A\oplus B) = \mu(A) + \mu(B)\).
scientific article; zbMATH DE number 6006169