ABSTRACT
Chapter 1
Spectral Decomposition
This chapter gives a treatment of the spectral theory for bounded op-
erators, the main result being the Spectral Decomposition Theorem.
Spectral sets of nite type are discussed in detail. While the develop-
ment of the adjoint space is along the classical lines, the product space
structure is used to introduce the Gram product of a nite set of el-
ements in the space with a nite set of elements in the adjoint space.
The product space structure also allows an integral representation of the
block reduced resolvent.
