Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent

Abstract

Our first aim is to clarify the results obtained by Lidskii devoted to the decomposition on the root vector system of the non-selfadjoint operator. We use a technique of the entire function theory and introduce a so-called Schatten–von Neumann class of the convergence exponent. Considering strictly accretive operators satisfying special conditions formulated in terms of the norm, we construct a sequence of contours of the power type that contrasts the results by Lidskii, where a sequence of contours of the exponential type was used.

Keywords

• strictly accretive operator
• Abel–Lidskii basis property
• Schatten–von Neumann class
• convergence exponent
• counting function