Bounds for Determinants of Linear Operators and their Applications

Before his retirement in 2009, Michael I. Gil′ was a professor at the Ben Gurion University of the Negev, Beer Sheva, Israel. He has authored more than 250 articles in scientific journals and 9 books.

• Preliminaries. Determinants of Schatten-Von Neumann Operators. Determinants of Nakano Type Operators. Determinants of Orlicz Type Operators. Determinants of p-summing Operators. Multiplicative Representations of Resolvents. Inequalities Between Determinants and Resolvents. Bounds for Eigenvalues and Determinants Via Self-commutators.Discrete Spectra of Compactly Perturbed Bounded Operators. Operators on Tensor Products of Euclidean Spaces and Matrix Equations. Two-parameter Matrix Eigenvalue Problem. Differential, Difference and Functional-differential equations

"[This] book is well written and some long computations are presented in a convincing manner. This book will surely be useful to specialists in operator theory, as well as to those interested in its applications, especially for the treatment of the determinants associated to Nakano and Orlicz type operators, among others. Graduate students may also be interested in some chapters of this work, in particular those containing improvements of certain classical results."- F.-H. Vasilescu, Mathematical Reviews, August 2017