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The parabolic algebra revisited

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The parabolic algebra revisited. / Kastis, Eleftherios; Power, Stephen.
In: Israel Journal of Mathematics, Vol. 259, No. 2, 01.03.2024, p. 559-587.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Kastis, E & Power, S 2024, 'The parabolic algebra revisited', Israel Journal of Mathematics, vol. 259, no. 2, pp. 559-587. https://doi.org/10.1007/s11856-023-2550-4

APA

Kastis, E., & Power, S. (2024). The parabolic algebra revisited. Israel Journal of Mathematics, 259(2), 559-587. https://doi.org/10.1007/s11856-023-2550-4

Vancouver

Kastis E, Power S. The parabolic algebra revisited. Israel Journal of Mathematics. 2024 Mar 1;259(2):559-587. Epub 2023 Oct 9. doi: 10.1007/s11856-023-2550-4

Author

Kastis, Eleftherios ; Power, Stephen. / The parabolic algebra revisited. In: Israel Journal of Mathematics. 2024 ; Vol. 259, No. 2. pp. 559-587.

Bibtex

@article{69a41a166b7b472aa9bd722eab9b9c13,
title = "The parabolic algebra revisited",
abstract = "The parabolic algebra Ap is the weakly closed operator algebra on L2(ℝ) generated by the unitary semigroup of right translations and the unitary semigroup of multiplication by the analytic exponential functions eiλx, λ≥0. It is reflexive, with an invariant subspace lattice LatAp which is naturally homeomorphic to the unit disc (Katavolos and Power, 1997). The structure of LatAp is used to classify strongly irreducible isometric representations of the partial Weyl commutation relations. A formal generalisation of Arveson{\textquoteright}s notion of a synthetic commutative subspace lattice is given for general subspace lattices, and it is shown that LatAp is not synthetic relative to the H∞(ℝ) subalgebra of Ap. Also, various new operator algebras, derived from isometric representations and from compact perturbations of Ap, are defined and identified.",
keywords = "operator algebra, semigroups of isometries, synthetic subspace lattice, compact perturbations",
author = "Eleftherios Kastis and Stephen Power",
year = "2024",
month = mar,
day = "1",
doi = "10.1007/s11856-023-2550-4",
language = "English",
volume = "259",
pages = "559--587",
journal = "Israel Journal of Mathematics",
issn = "0021-2172",
publisher = "Springer New York LLC",
number = "2",

}

RIS

TY - JOUR

T1 - The parabolic algebra revisited

AU - Kastis, Eleftherios

AU - Power, Stephen

PY - 2024/3/1

Y1 - 2024/3/1

N2 - The parabolic algebra Ap is the weakly closed operator algebra on L2(ℝ) generated by the unitary semigroup of right translations and the unitary semigroup of multiplication by the analytic exponential functions eiλx, λ≥0. It is reflexive, with an invariant subspace lattice LatAp which is naturally homeomorphic to the unit disc (Katavolos and Power, 1997). The structure of LatAp is used to classify strongly irreducible isometric representations of the partial Weyl commutation relations. A formal generalisation of Arveson’s notion of a synthetic commutative subspace lattice is given for general subspace lattices, and it is shown that LatAp is not synthetic relative to the H∞(ℝ) subalgebra of Ap. Also, various new operator algebras, derived from isometric representations and from compact perturbations of Ap, are defined and identified.

AB - The parabolic algebra Ap is the weakly closed operator algebra on L2(ℝ) generated by the unitary semigroup of right translations and the unitary semigroup of multiplication by the analytic exponential functions eiλx, λ≥0. It is reflexive, with an invariant subspace lattice LatAp which is naturally homeomorphic to the unit disc (Katavolos and Power, 1997). The structure of LatAp is used to classify strongly irreducible isometric representations of the partial Weyl commutation relations. A formal generalisation of Arveson’s notion of a synthetic commutative subspace lattice is given for general subspace lattices, and it is shown that LatAp is not synthetic relative to the H∞(ℝ) subalgebra of Ap. Also, various new operator algebras, derived from isometric representations and from compact perturbations of Ap, are defined and identified.

KW - operator algebra

KW - semigroups of isometries

KW - synthetic subspace lattice

KW - compact perturbations

U2 - 10.1007/s11856-023-2550-4

DO - 10.1007/s11856-023-2550-4

M3 - Journal article

VL - 259

SP - 559

EP - 587

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 2

ER -