On quasi $*$-paranormal operators

Mecheri, Salah

doi:10.15352/afa/1399900025

Cited by 10 publications

(9 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof, This is a direct consequence of theorems 2.8 and 3.4 of [4]. Proof, By using the results of [10] and Theorem 2.3 we get the proof.…”

Section: Some Applicationsmentioning

confidence: 73%

Some sub-classes of paranormal weighted conditional type operators

Estaremi¹

2016

Publ. Math. Debrecen

View full text Add to dashboard Cite

In this paper, some sub-classes of paranormal weighted conditional expectation type operators, such as * -paranormal, quasi- * -paranormal and (n, k)-quasi- * -paranormal weighted conditional expectation type operators on L 2 (Σ) are investigated. Also, some applications about the spectrum, point spectrum, joint point spectrum, approximate point spectrum and joint approximate point spectrum of these classes are presented.2010 Mathematics Subject Classification. 47B20.

show abstract

“…Proof, This is a direct consequence of theorems 2.8 and 3.4 of [4]. Proof, By using the results of [10] and Theorem 2.3 we get the proof.…”

Section: Some Applicationsmentioning

confidence: 73%

Some sub-classes of paranormal weighted conditional type operators

Estaremi¹

2016

Publ. Math. Debrecen

View full text Add to dashboard Cite

show abstract

“…If k = 0, it is clear that T is n- * -paranormal operator [8] and if n = 1, then T is * -paranormal [1]. Also, if n = 0, T is k quasi-hyponormal [8] and if n = 1, T is k-quasi- * -hyponormal operator [19].…”

Section: Definitionmentioning

confidence: 99%

“…Many authors extended this theorem for different non-normal classes of operators (see [2,[4][5][6][7][8][9][10][11][12]). In this paper, we shall generalize this theorem to certain (n, k)-quasi- * -paranormal operators.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Putnam-Fuglede Theorem for (n,k)-Quasi-∗-Paranormal Operators

Bachir

Segres

2019

Symmetry

View full text Add to dashboard Cite

T ∈ B ( H ) is said to be ( n , k ) -quasi-∗-paranormal operator if, for non-negative integers k and n, ∥ T ∗ ( T k x ) ∥ ( 1 + n ) ≤ ∥ T ( 1 + n ) ( T k x ) ∥ ∥ T k x ∥ 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 .

show abstract

“…• quasi- * -paranormal if ||T 2 (T x)|| 1/2 ||T x|| 1/2 ≥ ||T * (T x)|| for all x ∈ H (see [19]). • k-quasi- * -paranormal if ||T 2 (T k x)|| 1/2 ||T k x|| 1/2 ≥ ||T * (T k x)|| for all x ∈ H .…”

Section: Introductionmentioning

confidence: 99%

On $$(n,k)$$ ( n , k ) -Quasi- $$*$$ ∗ -paranormal Operators

Zeng

Zhong

2015

Bull. Malays. Math. Sci. Soc.

View full text Add to dashboard Cite

For nonnegative integers n and k, we introduce in this paper a new class of (n, k)-quasi- * -paranormal operators satisfyingThis class includes the class of n- * -paranormal operators and the class of (1, k)-quasi- * -paranormal operators contains the class of k-quasi- * -class A operators. We study the basic properties of (n, k)-quasi- * -paranormal operators, like relations of this new class of operators with other classes known in the literature, their matrix representation, and properties of their spectra.

show abstract

On quasi $*$-paranormal operators

Cited by 10 publications

References 0 publications

Some sub-classes of paranormal weighted conditional type operators

Some sub-classes of paranormal weighted conditional type operators

Asymmetric Putnam-Fuglede Theorem for (n,k)-Quasi-∗-Paranormal Operators

On $$(n,k)$$ ( n , k ) -Quasi- $$*$$ ∗ -paranormal Operators

Contact Info

Product

Resources

About