On Positive-Normal Operators

Jeon, In-Ho; Kim, Sehee; Ko, Eungil; Park, Ji‐Eun

doi:10.4134/bkms.2002.39.1.033

Cited by 10 publications

(3 citation statements)

References 6 publications

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“…If B(H) denotes the set of all bounded linear operators on a Hilbert space H, then A ∈ B(H) is said to be supraposinormal if AQA * = A * P A for some pair of positive operators Q, P ∈ B(H), where at least one of P , Q has dense range (see [11]). The operator A is posinormal (see [3], [4], [5]) if AA * = A * P A for some positive operator P ∈ B(H), called the interrupter. The operator A is coposinormal if A * is posinormal.…”

Section: Introductionmentioning

confidence: 99%

Posinormality, Coposinormality, and Supraposinormality for Some Triangular Operators

Rhaly¹

2016

SJM

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The range inclusion criterion for posinormality is studied in order to classify more examples of lower triangular factorable matrices as posinormal operators or not. Also, coposinormality is shown to be a hereditary property for lower triangular operators on 2 , and this leads to some results involving the posispectrum. Finally, sufficient conditions are given for lower triangular factorable matrices to be supraposinormal, and an example is given of a lower triangular factorable matrix that is supraposinormal but neither posinormal nor coposinormal. The last two sections also contain more general results that apply to operators on abstract Hilbert spaces.

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Section: Introductionmentioning

confidence: 99%

Posinormality, Coposinormality, and Supraposinormality for Some Triangular Operators

Rhaly¹

2016

SJM

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“…Posinormal operators were first introduced and studied by H. C. Rhaly [30] and have also been studied by some authors; see, for instance, the papers by M. Itoh [18] and by I. H. Jeon, S. H. Kim, E. Ko [17] , S.Mecheri [25] and B. P. Duggal and C. Kubrusly [12] , A. Bucur [6].…”

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

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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

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“…An interesting question is the following: Since (as alluded to in the introduction) there have been many generalizations of the Fuglede-Putnam theorem to non-normal operators, then can we prove it for posinormal operators? This notion appeared in [10,16].…”

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confidence: 99%

Yet More Versions of the Fuglede–putnam Theorem

Mortad¹

2009

Glasgow Math. J.

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Abstract. We give two types of generalisation of the well-known Fuglede-Putnam theorem. The paper is 'spiced up' with some examples and applications.2000 Mathematics Subject Classification. Primary 47A62, 47A99; Secondary 47B20. It is also worth mentioning that the author, in a previous work [11], gave a generalization of the Fuglede-Putnam theorem where all the operators involved were unbounded.The classical and most known form of the Fuglede-Putnam theorem is the following.

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On Positive-Normal Operators

Cited by 10 publications

References 6 publications

Posinormality, Coposinormality, and Supraposinormality for Some Triangular Operators

Posinormality, Coposinormality, and Supraposinormality for Some Triangular Operators

Positive-normal operators in semi-Hilbertian spaces

Yet More Versions of the Fuglede–putnam Theorem

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