Posinormal operators

Rhaly, H. C.

doi:10.2969/jmsj/04640587

Cited by 32 publications

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“…Let H be an infinite dimensional complex Hilbert space and B(H) denote the algebra of all bounded linear operators acting on H. Every operator T can be decomposed into T =U |T | with a partial isometry U , where |T |= √ T * T . In [8], H.C. Rhaly Jr. introduced and studied posinormal operators. He showed a characterization of posinormality and spectral properties of posinormal operators.…”

Section: Introductionmentioning

confidence: 99%

\mathversion{bold}SPECTRAL CONTINUITY OF $(p,k)$-QUASIPOSINORMAL OPERATOR AND $(p,k)$-QUASIHYPONORMAL OPERATOR

Kumar¹,

Kiruthika²

2013

Int. J. of Appl. Math.

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An operator T ∈ B(H) is said to be (p, k)-quasiposinormal operator, if T * k (c 2 (T * T ) p − (T T * ) p )T k ≥ 0 for a positive integer 0 < p ≤ 1, some c > 0 and a positive integer k. In this paper, we prove that, the (p, k) quasi-posinormal operator is a pole of resolvent of T * . Then we prove that if {T n } is a sequence of operators in the class (p, k) − Q and (p, k) − QP which converges in the operator norm topology to an operator T in the same class, then the functions spectrum, Weyl spectrum, Browder spectrum and essential surjectivity spectrum are continuous at T .

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Section: Introductionmentioning

confidence: 99%

\mathversion{bold}SPECTRAL CONTINUITY OF $(p,k)$-QUASIPOSINORMAL OPERATOR AND $(p,k)$-QUASIHYPONORMAL OPERATOR

Kumar¹,

Kiruthika²

2013

Int. J. of Appl. Math.

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“…In recent years this class has been generalized, in some sense, to the larger sets of so-called p-hyponormal, log-hyponormal, posinormal, k-quasihyponormal, etc. (see [l], [17], [15] and [8]). Results obtained about these operators show that they preserve many properties of hyponormal operators, such as the existence of functional models, decomposability, spectral properties etc.…”

Section: Introductionmentioning

confidence: 99%

“…-posinormal iff Im(T) C Im(T*), or equivalently TT* < A2T*T (see [15]); In [15], H.C.Rhaly proved that the class of all operators with the property that T -zI is posinormal for all z E C coinsides with the class of dominant operators (studied by J.Stampfii and Wadhwa; see [16]). The following inclusions hold hyponormal C M -hyponormal C posinormal C P -posinormal hyponormal C M -hyponormal C totally P -posinormal.…”

Section: Introductionmentioning

confidence: 99%

Totally P-posinormal operators are subscalar

Nickolov

Zhelev

2002

Integr equ oper theory

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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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Posinormal operators

Cited by 32 publications

References 0 publications

\mathversion{bold}SPECTRAL CONTINUITY OF $(p,k)$-QUASIPOSINORMAL OPERATOR AND $(p,k)$-QUASIHYPONORMAL OPERATOR

\mathversion{bold}SPECTRAL CONTINUITY OF $(p,k)$-QUASIPOSINORMAL OPERATOR AND $(p,k)$-QUASIHYPONORMAL OPERATOR

Totally P-posinormal operators are subscalar

Positive-normal operators in semi-Hilbertian spaces

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