![]() $$||A||= \sup\)$ which is a weaker condition than $\psi \in D(A)$. linear spaces, quickly specialise to Hilbert spaces and to get to the spectral theorem for (bounded as well as unbounded) oper-ators on separable Hilbert space. Let H 1 H 2be Hilbert spaces and T : dom(T) H 2be a denselydenedlinearoperator, i.e. Boundedness is equivalent to the fact that the range of values the observable, i.e., the spectrum $\sigma(A)$ of the associated operator $A$, is bounded in view of the spectral radius identity, The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of -algebra. Unbounded operators on Hilbert spaces Denition 1.1. In 25, the author considered the case where A is self-adjoint. Well often also meet infinite dimensional vector spaces that are spaces of functions, such as the wavefunctions you dealt. ![]() ![]() Some relevant self-adjoint operators in QM, like orthogonal projectors, are bounded actually, but these are very few in QM. Recently, the question of stabilization of bilinear systems with unbounded control operator has been treated in 25262728. ![]()
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