Spectrum of inner product type integral transformers on Hilbert spaces

Abstract

In this paper,  we have determined the spectrum of inner product type integral transformers on the Hilbert spaces. This has been achieved using the abelian properties of sets and the concept of commutators as in the von Neumann algebras.  We have also shown that the spectrum of the inner product type integral transformers is contained in the closure of its numerical range using the classical spectral inclusion theorem.