Elementary operators on Banach algebras and Fourier transform

• Autorzy: Miloš Arsenović , Dragoljub Kečkić
• Języki publikacji: EN

Abstrakty

EN

We consider elementary operators $x ↦ ∑_{j=1}^{n} a_{j}xb_{j}$, acting on a unital Banach algebra, where $a_{j}$ and $b_{j}$ are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families ${a_{j}}$ and ${b_{j}}$, i.e. $a_{j} = a_{j}' + ia_{j}''$ ($b_{j} = b_{j}' + ib_{j}''$), where all $a_{j}'$ and $a_{j}''$ ($b_{j}'$ and $b_{j}''$) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class of $C_{cpt}^{∞}$ functions on $ℝ^{2n}$.

Kategorie tematyczne

• 47B48: Operators on Banach algebras
• 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 173
• Numer: 2
• Strony: 149-166

Daty

wydano

2006

Twórcy

autor

Miloš Arsenović

• Matematički Fakultet, Univerzitet u Beogradu, Studentski trg 16-18, 11000 Beograd, Serbia and Montenegro

autor

Dragoljub Kečkić

• Matematički Fakultet, Univerzitet u Beogradu, Studentski trg 16-18, 11000 Beograd, Serbia and Montenegro

Identyfikatory

DOI

10.4064/sm173-2-3