This book is devoted to norm estimates for operator-valued
functions of one and two operator arguments, as well as to their
applications to spectrum perturbations of operators and to linear
operator equations, i.e. to equations whose solutions are linear
operators. Linear operator equations arise in both mathematical
theory and engineering practice. The norm estimates suggested in
the book have applications to the theories of ordinary
differential, difference, functional-differential and
integro-differential equations, as well as to the theories of
integral operators and analytic functions. This book provides new
tools for specialists in matrix theory and functional analysis. A
significant part of the book covers the theory of triangular
representations of operators that was developed by L de Branges, M
S Brodskii, I C Gohberg, M G Krein, M S Livsic and other
mathematicians.
General
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