The structure of doubly non-commuting isometries

Jeu, Marcel de; Pinto, Paulo R.

doi:10.1016/j.aim.2020.107149

Cited by 22 publications

(28 citation statements)

References 9 publications

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“…Using the above corollary, we can easily prove the results [5, Corollary 2.4], [22, Theorem 1.9] and [6,Theorem 3.4] in the following remark:…”

Section: The Generating Wandering Subspace Property and T I | H A Is A Unitary (Ie T I | H A Is Row Isometry And Cuntz Row Isometry) Whenmentioning

confidence: 80%

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Doubly commuting invariant subspaces for representations of product systems of $$C^*$$-correspondences

Trivedi

Veerabathiran

2021

Ann. Funct. Anal.

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We obtain a Shimorin Wold-type decomposition for a doubly commuting covariant representation of a product system of C * -correspondences over ℕ k 0 . This result gives Shimorin-type decompositions of recent Wold-type decompositions by Jeu and Pinto (Adv Math 368:107-149, 2020) for the q-doubly commuting isometries and by Popescu (J Funct Anal 279:108798, 2020) for Doubly Λ-commuting row isometries. Application to the wandering subspaces of the induced representations is explored, and a version of the Beurling-Lax-type characterization is obtained to study doubly commuting invariant subspaces.

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“…Using the above corollary, we can easily prove the results [5, Corollary 2.4], [22, Theorem 1.9] and [6,Theorem 3.4] in the following remark:…”

Section: The Generating Wandering Subspace Property and T I | H A Is A Unitary (Ie T I | H A Is Row Isometry And Cuntz Row Isometry) Whenmentioning

confidence: 80%

“…Let K be a closed subspace of H, then it is easy to see that where A ⊆ I m and ∈ ℕ A 0 . This combined with the following corollary, which is a generalization of [6,Theorem 3.4], [22,Theorem 1.9] and [25,Theorem 2.4].…”

Section: Corollary 34mentioning

confidence: 93%

Doubly commuting invariant subspaces for representations of product systems of $$C^*$$-correspondences

Trivedi

Veerabathiran

2021

Ann. Funct. Anal.

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“…The case |q ij | = 1 was studied in [25,32,46]. It was shown that E {qij } is nuclear for any such family {q ij } and the Fock representation is faithful.…”

Section: E Qmentioning

confidence: 99%

“…Indeed, recall that the tensor product of C(S 1 ) ⊗ C(S 1 ) does admit twists, the famous rotation algebra A q being the result. Also twists of tensor products of Toeplitz algebras have been considered [25,54]. However, the tensor product of Cuntz algebras may not be twisted as we will see.…”

Section: The Multiparameter Casementioning

confidence: 99%

“…Other objects of studies, closely related to the ones mentioned above, are C * -algebras generated by isometries, such as Cuntz algebras, extensions of noncommutative tori and their multi-parameter generalizations, see, [9,10,25,45,46]. The problems of classification of representations, existence of faithful (universal) representation, as well as the a study of structure of corresponding C * -algebra and dependence of C * -isomorphism classes on parameter of the deformations are among the central ones in this area.…”

Section: Introductionmentioning

confidence: 99%

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On $q$-tensor products of Cuntz algebras

Kuźmin¹,

Ostrovskyi²,

Proskurin³

et al. 2021

Preprint

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To 75-th birthday of our teacher Yurii S. SamoilenkoWe consider the C * -algebra E q n,m , which is a q-twist of two Cuntz-Toeplitz algebras. For the case |q| < 1, we give an explicit formula which untwists the q-deformation showing that the isomorphism class of E q n,m does not depend on q. For the case |q| = 1, we give an explicit description of all ideals in E q n,m . In particular, we show that E q n,m contains a unique largest ideal Mq. We identify E q n,m /Mq with the Rieffel deformation of On ⊗ Om and use a K-theoretical argument to show that the isomorphism class does not depend on q. The latter result holds true in a more general setting of multiparameter deformations.

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Smart Development of Ahmedabad-Gandhinagar Twin City Metropolitan Region, Gujarat, India

Bhatt

Jani

2018

Advances in 21st Century Human Settlements

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In this article, we prove K-stability for a family of C * -algebras, which are generated by a finite set of unitaries and isometries satisfying twisted commutation relations. This family includes the C * -algebra of doubly non-commuting isometries and free twist of isometries. Next, we consider the C * -algebra A V generated by an n-tuple of U-twisted isometries V with respect to a fixed n 2 -tuple U = {U ij : 1 ≤ i < j ≤ n} of commuting unitaries (see [6]). Under the assumption that the spectrum of the commutative C * -algebra generated by ({U ij : 1 ≤ i < j ≤ n}) does not contain any element of finite order in the torus group T ( n 2 ) , we show that A V is K-stable. Finally, we prove the same result for the C * -algebra generated by a tuple of free U-twisted isometries.

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The structure of doubly non-commuting isometries

Cited by 22 publications

References 9 publications

Doubly commuting invariant subspaces for representations of product systems of $$C^*$$-correspondences

Doubly commuting invariant subspaces for representations of product systems of $$C^*$$-correspondences

On $q$-tensor products of Cuntz algebras

Smart Development of Ahmedabad-Gandhinagar Twin City Metropolitan Region, Gujarat, India

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