Joint spectrum and unbounded operator algebras

Huang, Danrun; Zhang, Dianzhou

doi:10.1007/bf02582028

Cited by 3 publications

(7 citation statements)

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“…We shall call si and °U the GB*-algebra and the EC*-algebra generated by A = (A u ...,A n ) respectively. In [9] we proved the following …”

Section: Spm) Jmentioning

confidence: 85%

“…The definitions here have their background in the multiparameter spectral theory (Sleeman [6]), and are closely connected with Taylor's joint spectrum of A (see [9] and Section 5). be a commuting n-tuple of normal operators, the joint numerical range of A is the set W(A) in C such that where D(Aj) is the domain of A h i= 1,...,n.…”

Section: A Closed Operator T On H Is Said To Be Normal If T Is Denselmentioning

confidence: 99%

“…We know already from [9] that si is a GB*-algebra as defined in G. Allan [8], whose topology is given by a collection of seminorms:…”

Section: Spm) Jmentioning

confidence: 99%

“…It seems that one must consider unbounded operator algebras. Some work has been done in this direction for the joint spectrum of unbounded normal operators [9]. In the last section of this paper, we provide some intimate relations between the joint numerical range and the unbounded operator algebras for unbounded normal operators.…”

Section: Introductionmentioning

confidence: 99%

“…The definitions here have their background in the multiparameter spectral theory (Sleeman [6]), and are closely connected with Taylor's joint spectrum of A (see [9] and Section 5).…”

Section: Introductionmentioning

confidence: 99%

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Joint numerical ranges for unbounded normal operators

Huang

1985

Proceedings of the Edinburgh Mathematical Society

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For bounded operators, the theory of the joint numerical range has been developed by various authors [1,2,3,4,5]. Especially, the properties of commuting normal n-tuples are discussed in detail. Our purpose here is to show that many results in the above references still hold in the case of unbounded normal operators (see Theorem 2.3, Corrollary 3.5, Theorem 4.1, Theorem 4.2). Besides, the operator algebras are closely related to the theory of joint spectrum and joint numerical ranges in the boundedcase (cf. [1,3]). How about unbounded operators? It seems that one must consider unbounded operator algebras. Some work has been done in this direction for the joint spectrum of unbounded normal operators [9]. In the last section of this paper, we provide some intimate relations between the joint numerical range and the unbounded operator algebras for unbounded normal operators.

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“…We shall call si and °U the GB*-algebra and the EC*-algebra generated by A = (A u ...,A n ) respectively. In [9] we proved the following …”

Section: Spm) Jmentioning

confidence: 85%

Section: A Closed Operator T On H Is Said To Be Normal If T Is Denselmentioning

confidence: 99%

“…We know already from [9] that si is a GB*-algebra as defined in G. Allan [8], whose topology is given by a collection of seminorms:…”

Section: Spm) Jmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The definitions here have their background in the multiparameter spectral theory (Sleeman [6]), and are closely connected with Taylor's joint spectrum of A (see [9] and Section 5).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations