Bounds for Determinants of Linear Operators and their Applications

1. Auflage 2017
ISBN: 978-1-4987-9690-3
Verlag: Chapman and Hall/CRC

Buch, Englisch, 236 Seiten, Format (B × H): 156 mm x 235 mm, Gewicht: 476 g

Reihe: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

This book deals with the determinants of linear operators in Euclidean, Hilbert and Banach spaces. Determinants of operators give us an important tool for solving linear equations and invertibility conditions for linear operators, enable us to describe the spectra, to evaluate the multiplicities of eigenvalues, etc. We derive upper and lower bounds, and perturbation results for determinants, and discuss applications of our theoretical results to spectrum perturbations, matrix equations, two parameter eigenvalue problems, as well as to differential, difference and functional-differential equations.

Autoren/Hrsg.

Gil', Michael

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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

Über Autor(innen)

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.