Canonical decompositions induced by -contractions
Abstract
The classical Nagy-Foia\c s-Langer decomposition of an ordinary contraction is generalized in the context of the operators on a complex Hilbert space which, relative to a positive operator on , satisfy the inequality . As a consequence, a version of the classical von Neumann-Wold decomposition for isometries is derived in this context. Also one shows that, if and , then the decomposition of in normal part and pure part relative to is just a von Neumann-Wold type decomposition for , which can be completely described. As applications, some facts on the quasi-isometries recently studied in [4], [5], are obtained.
DOI Code:
10.1285/i15900932v28n2p187
Keywords:
A-contraction; A-isometry; quasi-isometry; von Neumann-Wold decomposition
Classification:
47A15; 47A63; 47B20
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