we define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital banach algebra a and show that the δ-approximate spectrum σ_δ (a) of a is compact. the relation between the δ-approximate spectrum and the usual spectrum is investigated. also an analogue of the classical gleason-kahane-zelazko theorem is established: for each ε>0, there is δ>0 such that if ϕ is...

In the setting of vector-valued quantum fields obeying a linear wave-equation in a globally hyperbolic, stationary spacetime, it is shown that the two-point functions of passive quantum states (mixtures of groundor KMS-states) fulfill the microlocal spectrum condition (which in the case of the canonically quantized scalar field is equivalent to saying that the two-point function is of Hadamard ...

It is well known that the spectrum condition, i.e. the positivity of the energy in every inertial coordinate system, is one of the central conceptual ingedients in model-independent approaches to relativistic quantum field theory. When one attempts to formulate quantum field theory in a model-independent manner on a curved background spacetime, it is not immediately clear which concepts replace...

A simple but powerful theoretical model for watermarking and attacks is presented. The attack consists of Wiener estimation of the watermark, followed by weighted feedback of the estimate to reduce the detector's correlation value. The Wiener attack is provably optimal, and it leads to the notion of energy-e cient watermarking, the generation of watermarks that resist Wiener estimation. It also...