Elementary operators on Banach algebras and Fourier transform

Miloš Arsenović, and Dragoljub Kečkić. "Elementary operators on Banach algebras and Fourier transform." Studia Mathematica 173.2 (2006): 149-166. <http://eudml.org/doc/284423>.

@article{MilošArsenović2006,
abstract = {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. $a_\{j\} = a_\{j\}^\{\prime \} + ia_\{j\}^\{\prime \prime \}$ ($b_\{j\} = b_\{j\}^\{\prime \} + ib_\{j\}^\{\prime \prime \}$), where all $a_\{j\}^\{\prime \}$ and $a_\{j\}^\{\prime \prime \}$ ($b_\{j\}^\{\prime \}$ and $b_\{j\}^\{\prime \prime \}$) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class of $C_\{cpt\}^\{∞\}$ functions on $ℝ^\{2n\}$.},
author = {Miloš Arsenović, Dragoljub Kečkić},
journal = {Studia Mathematica},
keywords = {Banach algebra; generalized scalar element; elementary operator; Fourier transform; Fuglede-Putnam theorem},
language = {eng},
number = {2},
pages = {149-166},
title = {Elementary operators on Banach algebras and Fourier transform},
url = {http://eudml.org/doc/284423},
volume = {173},
year = {2006},
}

TY - JOUR
AU - Miloš Arsenović
AU - Dragoljub Kečkić
TI - Elementary operators on Banach algebras and Fourier transform
JO - Studia Mathematica
PY - 2006
VL - 173
IS - 2
SP - 149
EP - 166
AB - 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. $a_{j} = a_{j}^{\prime } + ia_{j}^{\prime \prime }$ ($b_{j} = b_{j}^{\prime } + ib_{j}^{\prime \prime }$), where all $a_{j}^{\prime }$ and $a_{j}^{\prime \prime }$ ($b_{j}^{\prime }$ and $b_{j}^{\prime \prime }$) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class of $C_{cpt}^{∞}$ functions on $ℝ^{2n}$.
LA - eng
KW - Banach algebra; generalized scalar element; elementary operator; Fourier transform; Fuglede-Putnam theorem
UR - http://eudml.org/doc/284423
ER -