*A normal operator ( an operator that commutes with its adjoint ) on a Hilbert space generates a strongly continuous semigroup if and only if its spectrum is bounded from above.
32.
The statements of an application program are normal operators, which any single threaded program might consist of-they include variable assignments, conditional processing, loops, function calls, etc.
33.
The spectral theorem applies to self-adjoint operators and moreover, to normal operators, but not to densely defined, closed operators in general, since in this case the spectrum can be empty.
34.
The well-known Radon Nikodym theorem, the validity of the Poisson formula and the spectral theorem from the theory of normal operators can all be shown to follow as special cases of the Freudenthal spectral theorem.
35.
The same argument goes through for compact normal operators in infinite dimensional Hilbert spaces, where one make use of the Hilbert-Schmidt inner product, defined by tr ( " AB * " ) suitably interpreted.
36.
In turn, a User is both a " normal operator " ( an actor using the system for its intended purpose ) and a " functional beneficiary " ( a stakeholder who benefits from the use of the system ).
37.
Personnel applying to join the unit as JTAC operators undergo the same selection process as the normal operators, but do a shorter 8 month basic operator course, after which they continue with specialist training in the EOD or JTAC function.
38.
After Hilbert's initial formulation, the later development of abstract Hilbert space and the spectral theory of a single normal operator on it did very much go in parallel with the requirements of physics; particularly in the hands of von Neumann.
39.
Every generalized eigenvalue of a normal operator is thus genuine . ? is an eigenvalue of a normal operator " N " if and only if its complex conjugate \ overline { \ lambda } is an eigenvalue of " N * ".
40.
Every generalized eigenvalue of a normal operator is thus genuine . ? is an eigenvalue of a normal operator " N " if and only if its complex conjugate \ overline { \ lambda } is an eigenvalue of " N * ".
