Certain bounded linear operators T on a complex Hilbert space \h which have 2-isometric liftings S on another space \ka \supset \h are being investigated. We refer also to a more special type of liftings, as well as to those which additionally meet the condition S^*S\h \subset \h. Furthermore we describe other types of dilations for T, 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.

Additional Information


 Suciu, Laurian