The Weiss conjecture on admissibility of observation operators for contraction semigroups

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The Weiss Conjecture for Bounded Analytic Semigroups (2003, background): “This yields positive cases for the Weiss conjecture which are completely different from those considered so far in, for example, [10, 22].”
Transfer functions of regular linear systems. Part II: The system operator and the lax-phillips semigroup (2002, background): “Admissible control operators are a subspace of L(U ;X−1); we refer to [4], [9], [36], [38] and [43] for investigations of these operators.”
Admissibility of Control and Observation Operators for Semigroups: A Survey (2004, methodology): “Thus the Weiss conjecture holds for the right-shift semigroup, and soon afterwards the methods above were extended by Jacob and Partington [38] to give a generalization to the class of all contraction semigroups.”
On continuity of solutions for parabolic control systems and input-to-state stability (2017, result): “Although even in this case, counterexamples were found [16,17,41], there are situations with positive answers — most prominently, the case of contraction semigroups and U = C, [14], in which a connection with deep results in complex analysis appears.”
Observation and Control for Operator Semigroups (2009, background): “Introductions to functional analysis that stress the connections with and applications in systems theory are Nikolskii [178], Partington [181] and Young [240].”