@article{article_96779, title={On the Topological Centers of Banach Algebras}, journal={Gazi University Journal of Science}, volume={19}, pages={15–19}, year={2010}, author={Akay, Hayri and Soybaş, Danyal}, keywords={Topological center, Arens multiplication, Banach algebra, Left multiplier operator}, abstract={<p class="MsoNormal" style="margin: 0cm 3.6pt 0pt 0cm; text-align: justify;"> <span style="font-size: 8pt;"> <span style="font-family: Times New Roman;">Let A be a Banach algebra with a bounded approximate identity. Let </span> </span> <span style="position: relative; top: 6pt; mso-text-raise: -6.0pt;"> </span> <span style="font-size: 8pt;"> <span style="font-family: Times New Roman;"> <span style="mso-spacerun: yes;">  </span>and </span> </span> <span style="position: relative; top: 6pt; mso-text-raise: -6.0pt;"> </span> <span style="font-size: 8pt;"> <span style="font-family: Times New Roman;">be respectively, the topological centers of the algebras A** and (AA*)* with respect to the second Arens multiplication. In this paper, we show that </span> </span> <span style="position: relative; top: 6pt; mso-text-raise: -6.0pt;"> </span> <span style="font-size: 8pt;"> <span style="font-family: Times New Roman;">is isometrically isomorphic to LM(A) , where </span> </span> <span style="position: relative; top: 6pt; mso-text-raise: -6.0pt;"> </span> <span style="font-size: 8pt;"> <span style="font-family: Times New Roman;"> <span style="mso-spacerun: yes;">  </span>is a closed subalgebra of and LM(A) is the set of left multipliers operators of the Banach algebra A. </span> </span> </p> <p class="MsoNormal" style="margin: 0cm 3.6pt 0pt 0cm; text-align: justify;"> <span style="font-size: 8pt;"> <span style="font-family: Times New Roman;">  </span> </span> </p> <p class="MsoNormal" style="margin: 0cm 3.6pt 0pt 0cm; text-align: justify;"> <span style="font-family: Times New Roman;"> <strong style="mso-bidi-font-weight: normal;"> <span style="font-size: 8pt;">Key words: </span> </strong> <span style="font-size: 8pt;"> Topological center, Arens multiplication, Banach algebra, Left multiplier operator </span> </span> </p> <p>  </p>}, number={1}, publisher={Gazi University}