1302.2399 (Tomoki Mihara)

Spectral Theory for p-adic Banach Representations and p-adic Quantum
Theory    [PDF]

Tomoki Mihara

We established a new spectrum theory for p-adic Banach representations. We formulated in an explicit way the definition of the continuous functional calculus of a p-adic operator which is not necessarily analytic, is not bounded, or does not have the compact spectrum. It yields the notion of a p-adic normal operator with no use of an involusion, and one of the p-adic models of Quantum theory. As main theorems of this paper, we gave some sufficient conditions for the normality of p-adic operators. Such conditions are appliable to a bounded operator with good reduction property and a bounded operator possessing the intrinsic structure as a fractal.

View original: http://arxiv.org/abs/1302.2399