Polar decomposition and characterization of binormal operators

We illustrate the matrix representation of the closed range operator that enables us to determine the polar decomposition with respect to the orthogonal complemented submodules. This result proves that the reverse order law for the Moore-Penrose inverse of operators holds. Also, it is given some new characterizations of the binormal operators via the generalized Aluthge transformation. New characterizations of the binormal operators enable us to obtain equivalent conditions when the inner product of the binormal operator with its generalized Aluthge transformation is positive in the general setting of adjointable operators on Hilbert C*-modules.

Aluthge Transformation and *- Aluthge Transformation on M class Ak* Operator

Research works on Operators in Complex Hilbert spaces has been the interest of budding researchers in the recent years. In 1996, Furuta et al studied Aluthge transformation on phyponormal operators. Later, in 2001 yamazaki et al studied Aluthge transformation and powers of operators for class A(k)operator. This work was further carried over by Pannayappan et al and D.Senthil kumar et al. In this school work, we studied Aluthge transformation and *- Aluthge transformation for the new class of operator named M class Ak * operator on a non-zero Complex Hilbert space.

Aluthge Transformation of Quasi n-class Q and quasi n- class Q* Operators

In this paper, a new class of operators called quasi n-class Q and quasi n-class Q*operators are introduced and studied some properties. Quasi n-class Q and quasi n-class Q* composition and weighted composition operators on L2() and H2() are characterized. Also we discuss quasi n-class Q and quasi n-class Q composite multiplication operator on L2 space and Aluthge transformation of these class of operators are obtained.

Parallelism between Moore-Penrose inverse and Aluthge transformation of operators

In this paper we study some parallelisms between ?-Aluthge transform and binormal operators on a Hilbert space via the Moore-Penrose inverse. Moreover, we give some applications of these results on the Lambert multiplication operators acting on L2(?).