Weyl and Weyl type theorems for class Ak* and quasi class Ak* operators

quasi-normal Operator of order n

“…An operator T ∈ ℬ(ℋ) is said to be self-adjoint if T * = T, isomtry if T * T = I, unitary if T * T = TT * = I, where T * is the adjoint of T [2]. The operator T ∈ ℬ(ℋ) is called normal if TT * = T * T [1] , quasi-normal if T(T * T) = (T * T) T [6] , n-normal if T n T * = T * T n [1] , quasi n-normal if T(T * T n ) = (T * T n )T and n power quasi normal if T n (T * T) = (T * T)T n [5], where n is positive integer number. If S and T are bounded liner operator T on a Hilbert space H, then the operator S is said to be unitarily equivalent to T if there is a unitary operator U on H such that S =UTU * [4] , Let T∈B(H) and M is a closed subspace of H. Then M is called reduce of T if T (M) ⊆ M and T(M ⊥ )⊆M ⊥ , that is both M and M ⊥ are invariant under T and denoted by T/M [4] .…”

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

“…Later, Panayappan et al extended this concept and introduced class A k operators and verified Weyl's theorem [3]. In 2013, Panayappan et al introduced a new class of operators in a different manner called class A k * operator, quasi class A k * operators and studied Weyl and Weyl type theorems and also proved tensor product of two quasi class A k * operators are closed [4].…”