In this paper, the notion of Toeplitz Operators such as Toeplitz products analytic Toeplitz Operators and Hermitian Toeplitz Operators are discussed. In addition, spectral inclusion theorem for Toeplitz Operators and the spectrum and Eigenvalues of Hermitian Toeplitz Operators are explained in Hilbert space 1-!2

Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics