Contractive semigroup

Following Ref. [73] we describe first the steps before we comment on the mathematical results. Let us start with an isometric semigroup, G(f) t > 0, appropriately defined in the Hilbert space fi. If there exists a contractive semigroup SG t > 0 (defined on fi) and an invertible linear operator A, with its domain and range both dense in k, such that... 

There are in effect two principal consequences that we will examine. Firstly the spectral generalization [3] in terms of appearing complex poles of the actual resolvent, with the complex part interpreted essentially as the reciprocal life-time of the state and secondly the dynamical outcome regarding the time evolution, i.e. the conversion of an isometry to a contractive semigroup [18]. 

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