Abstract
In order to construct a Krein-space theory (i.e., a *-algebra of (unbounded) operators which are defined on a common, dense, and invariant domain in a Krein space) the cones of a-positivity and generalized a-positivity are considered in tensor algebras. The relations between these cones, algebraic #-cones, and involutive cones are investigated in detail. Furthermore, an example of a Pfunctional 0 defined on (C)® (tensor algebra over C) not being a-positive and yielding a non-trivial Krein-space theory is explicitely constructed. Thus, an affirmative answer to the question whether or not the method of P-functionals (introduced by Ota) is more general than the one of a-positivity (introduced by Jakobczyk) is provided in the case of tensor algebras. §
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