Some ergodic properties of multipliers on commutative Banach algebras
TURKISH JOURNAL OF MATHEMATICS, cilt.43, sa.3, ss.1721-1729, 2019 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 43 Sayı: 3
- Basım Tarihi: 2019
- Doi Numarası: 10.3906/mat-1812-110
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.1721-1729
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
A commutative semisimple regular Banach algebra Sigma(A) with the Gelfand space Sigma(A) is called a Ditkin algebra if each point of Sigma(A) boolean OR {infinity} is a set of synthesis for A. Generalizing the Choquet-Deny theorem, it is shown that if T is a multiplier of a Ditkin algebra A, then {phi is an element of A* : T* phi = phi} is finite dimensional if and only if card F-T is finite, where F-T = {gamma is an element of Sigma(A) : (T) over cap (gamma) = 1} and (T) over cap is the Helgason-Wang representation of T.