The spectrum of unbounded operators, typically acting in a complex Hilbert space, plays a vital role in diverse topics such as (i) mathematical formulation of quantum mechanics, (ii) the solution of Sturm-Liouville boundary differential equation, or (iii) asymptotic behaviour of 1-parametric strongly continuous operator semigroup.

We present our recent result on classification of additive spectrum preserving bijections on the set of unbounded operators. It turns out that every such map is nothing but a change of the domain. For important classes of Banach spaces, which include Hilbert and L_p spaces the same result is obtained even withohut injectivity.

The catalogues of such maps is handy at simplifications of problems which involve unbounded operaators and were asymptotics, say, is of vital importance.

This is a joint work with G. Dolinar, J. Marovt, and E. Poon.

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