On a decomposition for pairs of commuting contractions
A new decomposition of a pair of commuting, but not necessarily doubly commuting contractions is proposed. In the case of power partial isometries a more detailed decomposition is given.
On decomposition of pairs of commuting isometries
A review of known decompositions of pairs of isometries is given. A new, finer decomposition and its properties are presented.
On dilation and commuting liftings of n-tuples of commuting Hilbert space contractions
The n-tuples of commuting Hilbert space contractions are considered. We give a model of a commuting lifting of one contraction and investigate conditions under which a commuting lifting theorem holds for an n-tuple. A series of such liftings leads to an isometric dilation of the n-tuple. The method is tested on some class of triples motivated by Parrotts example. It provides also a new proof of the fact that a positive definite n-tuple has an isometric dilation.
Page 1