A+ CATEGORY SCIENTIFIC UNIT

Contractive homomorphisms of measure algebras and Fourier algebras

Volume 209 / 2012

Ross Stokke Studia Mathematica 209 (2012), 135-150 MSC: Primary 43A20, 43A10, 43A30, 43A22; Secondary 43A25. DOI: 10.4064/sm209-2-3

Abstract

We show that the dual version of our factorization [J. Funct. Anal. 261 (2011)] of contractive homomorphisms $\varphi : L^1(F) \rightarrow M(G)$ between group/measure algebras fails to hold in the dual, Fourier/Fourier–Stieltjes algebra, setting. We characterize the contractive $w^*\hbox {-}w^*$ continuous homomorphisms between measure algebras and (reduced) Fourier–Stieltjes algebras. We consider the problem of describing all contractive homomorphisms $\varphi : L^1(F) \rightarrow L^1(G)$.

Authors

  • Ross StokkeDepartment of Mathematics and Statistics
    University of Winnipeg
    515 Portage Avenue
    Winnipeg, Canada, R3B 2E9
    e-mail

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