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Gibbs states defined by biorthogonal sequences. (English) Zbl 1349.81098

Summary: Motivated by the growing interest in PT-quantum mechanics, in this paper we discuss some facts on generalized Gibbs states and their related KMS-like conditions. To achieve this, we first consider some useful connections between similar (Hamiltonian) operators and we propose some extended versions of the Heisenberg algebraic dynamics, deducing some of their properties that are useful for our purposes.

MSC:

81Q12 Nonselfadjoint operator theory in quantum theory including creation and destruction operators
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