On the Extension of B. Sz.-Nagy's Dilation Theorem to Linear Pencils of   Operators
  The explicit constructions of minimal isometric, and minimal unitary dilations of an arbitrary linear pencil of operators $T(\lambda)=T_0+\lambda T_1$ consisting of contractions on a separable Hilbert space for $|\lambda |=1$, which generalize the classical constructions (the case $T_1=0$), are presented. In contrast to the classical case these dilations are essentially non-unique. 
Dmitriy S. Kalyuzhniy