EAN: 9781461273745

AN INTRODUCTION TO MODELS AND DECOMPOSITIONS IN...

By a Hilbert-space operator we mean a bounded linear transformation be tween separable complex
Hilbert spaces. Decompositions and models for Hilbert-space operators have been very active
research topics in operator theory over the past three decades. The main motivation behind them
is the in variant subspace problem: does every Hilbert-space operator have a nontrivial
invariant subspace? This is perhaps the most celebrated open question in op erator theory. Its
relevance is easy to explain: normal operators have invariant subspaces (witness: the Spectral
Theorem)  as well as operators on finite dimensional Hilbert spaces (witness: canonical Jordan
form). If one agrees that each of these (i. e. the Spectral Theorem and canonical Jordan form)
is important enough an achievement to dismiss any further justification  then the search for
nontrivial invariant subspaces is a natural one  and a recalcitrant one at that. Subnormal
operators have nontrivial invariant subspaces (extending the normal branch)  as well as compact
operators (extending the finite-dimensional branch)  but the question remains unanswered even
for equally simple (i. e. simple to define) particular classes of Hilbert-space operators
(examples: hyponormal and quasinilpotent operators). Yet the invariant subspace quest has
certainly not been a failure at all  even though far from being settled. The search for
nontrivial invariant subspaces has undoubtly yielded a lot of nice results in operator theory 
among them  those concerning decompositions and models for Hilbert-space operators. This book
contains nine chapters.

Aktuelle Preise zur EAN 9781461273745

Produktinformationen zur 9781461273745