Description
Certain bounded linear operators 
on a complex Hilbert space 
which have 2-isometric liftings 
on another space 
are being investigated. We refer also to a more special type of liftings, as well as to those which additionally meet the condition 
. Furthermore we describe other types of dilations for , which are close to 2-isometries. Among these we refer to expansive (concave) operators and also to Brownian unitary dilations. Different matrix representations for such operators are obtained, where matrix entries involve contractive operators.
