On Wold-type decomposition

Pagacz, Patryk

doi:10.1016/j.laa.2011.09.001

Cited by 18 publications

(9 citation statements)

References 7 publications

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“…Each k * -paranormal operator is (k + 1)-paranormal (cf. [11,Proposition 4.8]), so T is a k-paranormal operator. Thus…”

Section: The Pf Property For K * -Paranormal Operatorsmentioning

confidence: 99%

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The Putnam-Fuglede property for paranormal and *-paranormal operators

Pagacz¹

2013

OpMath

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Abstract. An operator T ∈ B(H) is said to have the Putnam-Fuglede commutativity property (PF property for short) if T * X = XJ for any X ∈ B(K, H) and any isometry J ∈ B(K) such that T X = XJ * . The main purpose of this paper is to examine if paranormal operators have the PF property. We prove that k * -paranormal operators have the PF property. Furthermore, we give an example of a paranormal without the PF property.

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“…Each k * -paranormal operator is (k + 1)-paranormal (cf. [11,Proposition 4.8]), so T is a k-paranormal operator. Thus…”

Section: The Pf Property For K * -Paranormal Operatorsmentioning

confidence: 99%

“…In [11] we have shown that k-paranormal, k * -paranormal, (p, k)-quasihyponormal contractions and contractions of class Q have the PF property (see also [3,4,6]). Our main purpose is to answer the question: Which of the above mentioned operators (not necessarily contractions) have the PF property?…”

Section: Introductionmentioning

confidence: 99%

The Putnam-Fuglede property for paranormal and *-paranormal operators

Pagacz¹

2013

OpMath

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“…is (n, k)-quasiparanormal if and only if T ∈ k-Q A(n). Pagacz [13,Proposition 4.8] proved that the class of * -n-paranormal operators is a subclass of the class of (n + 1)-paranormal operators. Zeng and Zhong [19, Theorem 2.1] proved that * -(n, k)-quasiparanormal operators are (n+1, k−1)-quasiparanormal.…”

Section: Lemma 42 Letmentioning

confidence: 99%

“…An operator T belongs to class Q if 1 2 T 2 x 2 + 1 2 x 2 ≥ T x 2 for x ∈ H. It is known that the class Q contains the class of paranormal operators [13]. (2) Similarly, T * is of class Q if and only if T 2 T * 2 − 2T T * + I ≥ 0.…”

Section: Lemma 42 Letmentioning

confidence: 99%

Reducibility of Invariant Subspaces of Operators Related to k-Quasiclass-A(n) Operators

Yuan

Wang

2015

Complex Anal. Oper. Theory

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It is well-known that hyponormal operators have many interesting properties, for example, if the restriction T | M of the hyponormal operator T on its nontrivial closed invariant subspace M is normal, then M reduces T . In order to discuss the reducibility of invariant subspaces of an operator, four properties of invariant subspaces (R i , i = 1, . . . , 4) are introduced. Among others, it is proved that, for a k-quasi-A(n) operator T , if the restriction T | M is normal and injective, then M reduces T , thus the function σ : T −→ σ (T ) is continuous on the class of k-quasiclass-A(n) operators. Some examples related to class A(n) and n-paranormal operator are given which imply that the inclusion relations are strict.

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“…Consequently, T has to be a contraction. P. Pagacz showed that a contraction which belongs to the class Q, shares the PF property (see [40] and [38] for the paranormal case). This gives us that γ(A T * ,L ) > 0 is valid, which completes our proof.…”

Section: Proofsmentioning

confidence: 99%

Asymptotic behaviour of Hilbert space operators with applications

Gehér

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On Wold-type decomposition

Cited by 18 publications

References 7 publications

The Putnam-Fuglede property for paranormal and *-paranormal operators

The Putnam-Fuglede property for paranormal and *-paranormal operators

Reducibility of Invariant Subspaces of Operators Related to k-Quasiclass-A(n) Operators

Asymptotic behaviour of Hilbert space operators with applications

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