scholarly journals Yang–Baxter algebras, convolution algebras, and Grassmannians

2020 ◽  
Vol 75 (5) ◽  
pp. 791-842
Author(s):  
V. G. Gorbunov ◽  
C. Korff ◽  
C. Stroppel
Keyword(s):  
1990 ◽  
Vol 13 (3) ◽  
pp. 517-525 ◽  
Author(s):  
Hans G. Feichtinger ◽  
A. Turan Gürkanli

Continuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter's presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebrasLw1(G),Ga locally compact Abelian group. These spaces are defined by weightedLp-conditions of their Fourier transforms. In the first section invariance properties and asymptotic estimates for the translation and modulation operators are given. Using these it is possible to characterize inclusions in section 3 and to show that two spaces of this type coincide if and only if their parameters are equal. In section 4 the existence of approximate identities in these algebras is established, from which, among other consequences, the bijection between the closed ideals of these algebras and those of the corresponding Beurling algebra is derived.


1996 ◽  
Vol 79 ◽  
pp. 283 ◽  
Author(s):  
A. T. -m. Lau ◽  
R. J. Loy
Keyword(s):  

2002 ◽  
Vol 54 (2) ◽  
pp. 303-323 ◽  
Author(s):  
Fereidoun Ghahramani ◽  
Sandy Grabiner

AbstractWe study convergence in weighted convolution algebras L1(ω) on R+, with the weights chosen such that the corresponding weighted space M(ω) of measures is also a Banach algebra and is the dual space of a natural related space of continuous functions. We determine convergence factor ɳ for which weak*-convergence of {λn} to λ in M(ω) implies norm convergence of λn * f to λ * f in L1(ωɳ). We find necessary and sufficent conditions which depend on ω and f and also find necessary and sufficent conditions for ɳ to be a convergence factor for all L1(ω) and all f in L1(ω). We also give some applications to the structure of weighted convolution algebras. As a preliminary result we observe that ɳ is a convergence factor for ω and f if and only if convolution by f is a compact operator from M(ω) (or L1(ω)) to L1(ωɳ).


2020 ◽  
Vol 278 (11) ◽  
pp. 108468
Author(s):  
Mahmoud Filali ◽  
Pekka Salmi
Keyword(s):  

Author(s):  
D. G. Todd

In this paper we extend a result of Johnson and Lahr(3), which characterizes the multiplier algebra of L1(a, b) (the algebra of Lebesgue integrable functions on the interval of real numbers from a to b, under order convolution) to the L1 algebra of a general totally ordered semigroup. Similar work has been done in (l), but under more restrictive conditions.


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