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Elementary operators on Banach algebras and Fourier transform

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Arsenović M., Kečkić D.

Studia Mathematica

2006

tom 173

nr 2

149-166

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 $ℝ^{2n}$.

Ograniczanie wyników

1 Studia Mathematica

1 Arsenović M.

1 Kečkić D.

1 2006

Wyniki wyszukiwania

Elementary operators on Banach algebras and Fourier transform