2 research outputs found
Spectral properties of (m;n)-isosymmetric multivariable operators
Inspired by recent works on -isometric and -symmetric multivariables
operators on Hilbert spaces, in this paper we introduce the class of -isosymmetric multivariables operators. This new class of operators emerges
as a generalization of the -isometric and -isosymmetric multioperators.
We study this class of operators and give some of their basic properties. In
particular, we show that if is an -isosymmetric multioperators and is an -nilpotent multioperators,
then is an -isosymmetric
multioperators under suitable conditions. Moreover, we give some results about
the joint approximate spectrum of an -isosymmetric multioperators
Asymmetric Putnam-Fuglede Theorem for (n,k)-Quasi-β-Paranormal Operators
T ∈ B ( H ) is said to be ( n , k ) -quasi-∗-paranormal operator if, for non-negative integers k and n, β₯ T ∗ ( T k x ) β₯ ( 1 + n ) ≤ β₯ T ( 1 + n ) ( T k x ) β₯ β₯ T k x β₯ n ; for all x ∈ H . In this paper, the asymmetric Putnam-Fuglede theorem for the pair ( A , B ) of power-bounded operators is proved when (i) A and B ∗ are n-∗-paranormal operators (ii) A is a ( n , k ) -quasi-∗-paranormal operator with reduced kernel and B ∗ is n-∗-paranormal operator. The class of ( n , k ) -quasi-∗-paranormal operators properly contains the classes of n-∗-paranormal operators, ( 1 , k ) -quasi-∗-paranormal operators and k-quasi-∗-class A operators. As a consequence, it is showed that if T is a completely non-normal ( n , k ) -quasi-∗-paranormal operator for k = 0 , 1 such that the defect operator D T is Hilbert-Schmidt class, then T ∈ C 10