In this article, we give two different proofs of the existence of the minimal isometric dilation of a single contraction. Then using the existence of a unitary dilation of a contraction, we prove the `von Neumann's ...

A pair of commuting bounded operators (S; P ) acting on a Hilbert space, is called a -contraction, if it has the symmetrised bides = f(z1 + z2; z1z2) : jz1j 1; jz2j 1g C2 as a spectral set. For every -contraction (S; P ), ...

In a foundational paper “Operators Possesing an Open Set of Eigenvalues” written several decades ago, Cowen and Douglas showed that an operator T on a Hilbert space ‘H possessing an open set Ω C of eigenvalues determines ...

In this thesis we have investigated two different types of problems in multivariable operator theory. The first one deals with the defect sequence for contractive tuples and maximal con-tractive tuples. These condone deals ...

A pair of commuting bounded operators (S, P) for which the set r = {(z 1 +z 2,z 1z 2) : |z 1| ≤1, |z 2| ≤1} C2 is a spectral set, is called a r-contraction in the literature. For a contraction P and a bounded commutant ...

Let H be a separable Hilbert space over the complex field. The class S := {N|M : N is normal on H and M is an invariant subspace for Ng of subnormal operators. This notion was introduced by Halmos. The minimal normal ...