On (p,k)-quasihyponormal operators

Kim, In Hyoun

doi:10.7153/mia-07-61

Cited by 22 publications

(25 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[14,16,23]), that is, σ w (f (T )) = f (σ w (T )) when f ∈ H(σ(T )) where H(σ(T )) means the space of all functions f analytic on some open set G containing σ(T ). According to Corburn [8], we say that Weyl's theorem holds for an operator T if σ(T ) − σ w (T ) = π 00 (T ).…”

Section: Spectral Mapping Theorem On Weyl Spectrum Of N-paranormal Opmentioning

confidence: 99%

See 1 more Smart Citation

Weyl Spectrum of Class A(n) and n-Paranormal Operators

Yuan

Гао

2008

Integr. equ. oper. theory

View full text Add to dashboard Cite

Let n be a positive integer, an operator T belongs to class A(n) if |T 1+n | 2/(1+n) ≥ |T | 2 , which is a generalization of class A and a subclass of n-paranormal operators, i.e., T 1+n x 1/(1+n) ≥ T x for unit vector x. It is showed that if T is a class A(n) or n-paranormal operator, then the spectral mapping theorem on Weyl spectrum of T holds. If T belongs to class A(n), then the nonzero points of its point spectrum and joint point spectrum are identical, the nonzero points of its approximate point spectrum and joint approximate point spectrum are identical.

show abstract

Section: Spectral Mapping Theorem On Weyl Spectrum Of N-paranormal Opmentioning

confidence: 99%

“…Very recently, this theorem was shown to hold for several classes of operators including class A and paranormal operators (cf. [14,16,23,24]). Here, we shall prove the following result.…”

Section: Spectral Mapping Theorem On Weyl Spectrum Of N-paranormal Opmentioning

confidence: 99%

Weyl Spectrum of Class A(n) and n-Paranormal Operators

Yuan

Гао

2008

Integr. equ. oper. theory

View full text Add to dashboard Cite

show abstract

“…In [13], Duggal showed that if for non-zero T, S ∈ B(H), T ⊗ S is p-hyponormal if and only if T and S are p-hyponormal. Thus result was extended to p-quasihyponormal operators in [19].…”

Section: T S ∈ B(h) Let T ⊗ S ∈ B(h⊗h)mentioning

confidence: 99%

“…p-Hyponormal, p-posinormal, p-quasihyponormal, and (p, k)-quasihyponormal operators have been studied by many authors see for instance [19], [22] and references therein. and it is known that hyponormal operators have many interesting properties similar to those of normal operators( See [6], [7], [8]).…”

Section: It Is Known That T ∈ Ct P (H) If and Only If It Is Dominant mentioning

confidence: 99%

Positive-normal operators in semi-Hilbertian spaces

Jah¹,

Mahmoud²

2014

imf

View full text Add to dashboard Cite

Given a bounded positive linear operator A on a Hilbert space H we consider the semi-Hilbertian space (H , | A ), where ξ | η A := Aξ | η . In this paper we introduce a class of operators on a semi Hilbertian space H with inner product | A . We call the elements of this class A-positive-normal or A-posinormal. An operator T ∈ B(H) is said to be A-posinormal if there exists a A-positive operator P ∈ B(H) (i.e., AP ≥ 0) such that T AT * = T * AP T. We study some basic properties of these operators. Also we study the relationship between a special case of this class with the other kinds of classes of operators in semi-Hilbertian spaces.Mathematics Subject Classification: Primary 47A05, 47A30 Secondary 47A62

show abstract

“…Very recently, the theorem was shown to hold for several classes of operators including w-hyponormal operators and paranormal operators (cf. [17,32,20]). …”

Section: Weyl Spectrummentioning

confidence: 99%

Spectrum of Class wF(p,r,q) Operators

Yuan

Гао

2007

J. Inequal. Appl.

View full text Add to dashboard Cite

Dedicated to Professor Daoxing Xia on his 77th birthday with respect and affectionRecommended by Jozsef Szabados This paper discusses some spectral properties of class wF(p,r, q) operators for p > 0, r > 0, p + r ≤ 1, and q ≥ 1. It is shown that if T is a class wF(p,r, q) operator, then the Riesz idempotent E λ of T with respect to each nonzero isolated point spectrum λ is selfadjoint and* . Afterwards, we prove that every class wF (p,r, q) operator has SVEP and property (β), and Weyl's theorem holds for f (T) when f ∈ H(σ(T)).

show abstract

On (p,k)-quasihyponormal operators

Cited by 22 publications

References 18 publications

Weyl Spectrum of Class A(n) and n-Paranormal Operators

Weyl Spectrum of Class A(n) and n-Paranormal Operators

Positive-normal operators in semi-Hilbertian spaces

Spectrum of Class wF(p,r,q) Operators

Contact Info

Product

Resources

About