Spectral Invariance of $$*$$-Representations of Twisted Convolution Algebras with Applications in Gabor Analysis

作者：A. Austad · 发表于：Journal of Fourier Analysis and Applications · 年份：2020 · DOI：10.1007/s00041-021-09860-z · 被引用次数：10 · 研究领域：Mathematics

We show spectral invariance for faithful $$*$$ ∗ -representations for a class of twisted convolution algebras. More precisely, if G is a locally compact group with a continuous 2-cocycle c for which the corresponding Mackey group $$G_c$$ G c is $$C^*$$ C ∗ -unique and symmetric, then the twisted convolution algebra $$L^1 (G,c)$$ L 1 ( G , c ) is spectrally invariant in $${\mathbb {B}}({\mathcal {H}})$$ B ( H ) for any faithful $$*$$ ∗ -representation of $$L^1 (G,c)$$ L 1 ...