Unbounded Normal Operators in Hilbert Space
S. Kaniel · Transactions of the American Mathematical Society · 1964
In this work the author attempts to find "intermediates" between symmetric and general operators ; these are the unbounded normal operators.Unbounded normal operators are defined in Chapter 2. In addition to the commutative relations there are conditions imposed on the domains of a normal operator and its adjoint.Most of this chapter is devoted to theorems dealing with properties of such operators.In Chapter 3 the extensions of normal operators are considered.An important particular case is the complete normal extensions.These have an inverse which is a bounded normal operator.In this case there are theorems investigating the local behaviour of the spectrum, the asymptotic distribution of the eigenvalues, etc.Some theorems on general unbounded operators are obtained in the first chapter.Chapter 1.General Unbounded Operators