Weak* properties of weighted convolution algebras II

• Autorzy: Sandy Grabiner
• Języki publikacji: EN

Abstrakty

EN

We show that if ϕ is a continuous homomorphism between weighted convolution algebras on ℝ⁺, then its extension to the corresponding measure algebras is always weak* continuous. A key step in the proof is showing that our earlier result that normalized powers of functions in a convolution algebra on ℝ⁺ go to zero weak* is also true for most measures in the corresponding measure algebra. For some algebras, we can determine precisely which measures have normalized powers converging to zero weak*. We also include a variety of applications of weak* results, mostly to norm results on ideals and on convergence.

Kategorie tematyczne

• 46J20: Ideals, maximal ideals, boundaries
• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 46J45: Radical Banach algebras
• 43A10: Measure algebras on groups, semigroups, etc.
• 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 198
• Numer: 1
• Strony: 53-67

Daty

wydano

2010

Twórcy

autor

Sandy Grabiner

• Department of Mathematics, Pomona College, 610 North College Ave., Claremont, CA 91711, U.S.A.

Identyfikatory

DOI

10.4064/sm198-1-3