Inherited Properties Through the Helton Class of an Operator

Kim, Insook; Kim, Yoenha; Ko, Eungil; Lee, Eun Ji

doi:10.4134/bkms.2011.48.1.183

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Cited by 5 publications

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“…This relation is studied in [21] and [22] for bounded operators S and T on a Hilbert space. In this context, we say T is in the nth Helton class of S and write T ∈ Helton n (S) if γ n (S, T ) = 0.…”

Section: Introductionmentioning

confidence: 99%

Tensor-splitting properties of $n$-inverse pairs of operators

Paul

2017

Studia Math.

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In this paper we study n-inverse pairs of operators on the tensor product of Banach spaces. In particular we show that an n-inverse pair of elementary tensors of operators on the tensor product of two Banach spaces can arise only from l-and m-inverse pairs of operators on the individual spaces. This gives a converse to a result of Duggal and Müller [13], and proves a conjecture of the second named author [16]. Our proof uses techniques from algebraic geometry, which generalize to other relations among operators in a tensor product. We apply this theory to obtain results for n-symmetries in a tensor product as well.

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Section: Introductionmentioning

confidence: 99%

Tensor-splitting properties of $n$-inverse pairs of operators

Paul

2017

Studia Math.

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Extension of m‐Symmetric Hilbert Space Operators

Alshammari

2022

Journal of Mathematics

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We introduce a new class of operators, which we will call the class of P -quasi- m -symmetric operators that includes m -symmetric operators and k -quasi m -symmetric operators. Some basic structural properties of this class of operators are established based on the operator matrix representation associated with such operators.

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Asymptotic Intertwining by the Identity Operator and Permanence of Spectral Properties

Duggal¹

2013

Banach J. Math. Anal.

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Inherited Properties Through the Helton Class of an Operator

Abstract: Abstract. In this paper we show that Helton class preserves the nilpotent and finite ascent properties. Also, we show some relations on nontransitivity and decomposability between operators and their Helton classes. Finally, we give some applications in the Helton class of weighted shifts.

Cited by 5 publications

References 8 publications

Tensor-splitting properties of $n$-inverse pairs of operators

Tensor-splitting properties of $n$-inverse pairs of operators

Extension of m‐Symmetric Hilbert Space Operators

Asymptotic Intertwining by the Identity Operator and Permanence of Spectral Properties

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