Date of Award
Master of Science (MS)
Very often the operators that we study appear most naturally in highly non-diagonal representation. The main goal of spectral theory is to solve this problem by exhibiting for many operators a natural orthonormal basis with respect to which the operators have diagonal representations. However, this can be done only for certain classes of operators. The most important such class is probably the class of compact operators. The problem is that it is often hard to tell whether an operator is compact looking at its non-diagonal representation. In this thesis, we will study a class of operators for which we can determine all of their basic operator-theoretic properties from their original representation which is not diagonal in the classical sense. There are many important subclasses of operators which belong in our class, including Toeplitz operators on various function spaces, some pseudo-differential operators, some singular integral operators, etc.
Li, Haodong, "Multiplier Operator on Framed Hilbert Spaces" (2015). All Theses. 2263.