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- Alaghmandan, Mahmood, 1983, et al.
(författare)
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Completely bounded bimodule maps and spectral synthesis
- 2017
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Ingår i: International Journal of Mathematics. - : World Scientific Pub Co Pte Lt. - 0129-167X .- 1793-6519. ; 28:10
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Tidskriftsartikel (refereegranskat)abstract
- We initiate the study of the completely bounded multipliers of the Haagerup tensor product A(G) circle times(h) A(G) of two copies of the Fourier algebra A(G) of a locally compact group G. If E is a closed subset of G we let E# = {(s, t) : st. E} and show that if E# is a set of spectral synthesis for A(G) circle times(h) A(G) then E is a set of local spectral synthesis for A(G). Conversely, we prove that if E is a set of spectral synthesis for A(G) and G is a Moore group then E# is a set of spectral synthesis for A(G)circle times(h) A(G). Using the natural identification of the space of all completely bounded weak* continuous VN(G)' bimodule maps with the dual of A(G)circle times(h) A(G), we show that, in the case G is weakly amenable, such a map leaves the multiplication algebra of L-infinity(G) invariant if and only if its support is contained in the antidiagonal of G.
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| 4. |
- Bershtein, O., et al.
(författare)
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Maximum modulus principle for "holomorphic functions" on the quantum matrix ball
- 2019
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 276:5, s. 1479-1509
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Tidskriftsartikel (refereegranskat)abstract
- We describe the Shilov boundary ideal for a q-analog of the algebra of holomorphic functions on the unit ball in the space of n x n matrices and show that its C*-envelope is isomorphic to the C*-algebra of continuous functions on the quantum unitary group U-q(n). (C) 2018 Elsevier Inc. All rights reserved.
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| 6. |
- Ghandehari, M., et al.
(författare)
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Beurling-Fourier algebras on Lie groups and their spectra
- 2021
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 391
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Tidskriftsartikel (refereegranskat)abstract
- We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and their associated Beurling-Fourier algebras. Constructions of nontrivial weights will be presented focusing on the cases of representative examples of Lie groups, namely SU(n), the Heisenberg group H-r, the reduced Heisenberg group Hr, the Euclidean motion group E(2) and its simply connected cover (E) over tilde (2). We will determine the spectrum of Beurling-Fourier algebras on each of the aforementioned groups emphasizing its connection to the complexification of underlying Lie groups. We also demonstrate that "polynomially growing" weights do not change the spectrum and show the associated regularity of the resulting Beurling-Fourier algebras. (C) 2021 Elsevier Inc. All rights reserved.
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| 7. |
- Giselsson, Olof, 1986, et al.
(författare)
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Beurling-Fourier algebras and complexification
- 2024
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Ingår i: Advances in Mathematics. - 0001-8708 .- 1090-2082. ; 445
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we develop a new approach that allows to identify the Gelfand spectrum of weighted Fourier algebras as a subset of an abstract complexification of the corresponding group for a wide class of groups and weights. This generalizes recent related results of Ghandehari-Lee-Ludwig-Spronk-Turowska [11] about the spectrum of Beurling-Fourier algebras on some Lie groups. In the case of discrete groups we show that the spectrum of Beurling-Fourier algebra is homeomorphic to the group itself.
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| 8. |
- He, W. J., et al.
(författare)
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Completely Compact Herz-Schur Multipliers of Dynamical Systems
- 2022
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Ingår i: Journal of Fourier Analysis and Applications. - : Springer Science and Business Media LLC. - 1069-5869 .- 1531-5851. ; 28:3
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Tidskriftsartikel (refereegranskat)abstract
- We prove that if G is a discrete group and (A, G, alpha) is a C*-dynamical system such that the reduced crossed product A (sic)(r,alpha) G possesses property (SOAP) then every completely compact Herz-Schur (A, G, alpha)-multiplier can be approximated in the completely bounded norm by Herz-Schur (A, G, alpha)-multipliers of finite rank. As a consequence, if G has the approximation property (AP) then the completely compact Herz-Schur multipliers of A(G) coincide with the closure of A(G) in the completely bounded multiplier norm. We study the class of invariant completely compact Herz-Schur multipliers of A (sic)(r,alpha) G and provide a description of this class in the case of the irrational rotation algebra.
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