fa نتایجی در مورد همگرایی های غیرکراندار در مشبکه های باناخ ریاضی Mat علمی پژوهشی بنیادی S <strong><span dir="RTL">فرض کنید E &nbsp;یک مشبکه &nbsp;باناخ باشد. تور &nbsp;</span>(</strong> <strong><span dir="RTL">&nbsp; در </span>&nbsp;&nbsp;E<span dir="RTL">، همگرای ضعیف مطلق غیرکراندار ( uaw-همگرا )&nbsp; به </span></strong> <strong><span dir="RTL">&nbsp; گفته می شود در صورتی که &nbsp;برای هر عنصر مثبت </span>u<span dir="RTL">&nbsp; در E ،&nbsp; تور &nbsp;</span></strong> <strong><span dir="RTL">&nbsp; همگرای ضعیف به صفر باشد. در این مقاله، همگرایی &nbsp;ضعیف مطلق &nbsp;غیر کراندار را در E &nbsp;مورد بررسی بیشتر قرار می دهیم. خواهیم دید که این همگرای تحت ایده ال ها و زیر مشبکه ها، پایا می باشد. متناسب با un-همگرایی، نشان می دهیم uaw-همگرایی، توپولوژی ایجاد می کند، بدین معنی که E همراه با uaw-توپولوژی، تشکیل یک فضای برداری توپولوژیک می دهد. &nbsp;همچنین، چند نکته در مورد </span>-uaw <span dir="RTL">بسته بودن مجموعه ها را بیان می نماییم. با چند مثال، مفاهیم را ملموس تر مورد توجه قرار می دهیم. در نهایت، عملگرهای پیوسته قوی را بین مشبکه های باناخ معرفی کرده و برخی از خواص آن را بررسی می نماییم. به ویژه، مشبکه های باناخ با یکه قوی را بر حسب این دسته از عملگرها رده بندی می نماییم.</span></strong> <span style="line-height:22.0pt"><b><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">Introduction</span></span></b></span><br> <span style="font-size:11pt"><span style="line-height:22.0pt"><span style="text-autospace:none"><span style="font-family:Calibri,sans-serif"><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">Suppose E is a Banach lattice. A net </span></span><m:omath><i><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r>(</m:r></span></span></i><m:ssub><m:ssubpr><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><span style="font-style:italic"><m:ctrlpr></m:ctrlpr></span></span></span></m:ssubpr><m:e><i><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r>x</m:r></span></span></i></m:e><m:sub><i><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r>&alpha;</m:r></span></span></i></m:sub></m:ssub><i><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r>)</m:r></span></span></i></m:omath><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">&nbsp;in E is said to be unbounded absolute weak convergent (uaw-convergent, for short) to </span></span><m:omath><i><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r>x</m:r><m:r>&isin;</m:r><m:r>E</m:r></span></span></i></m:omath><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">&nbsp;provided that the net </span></span><m:omath><i><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r>(</m:r></span></span></i><m:d><m:dpr><m:begchr m:val="|"><m:endchr m:val="|"><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:ctrlpr></m:ctrlpr></span></span></m:endchr></m:begchr></m:dpr><m:e><m:ssub><m:ssubpr><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:ctrlpr></m:ctrlpr></span></span></m:ssubpr><m:e><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>x</m:r></span></span></m:e><m:sub><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>&alpha;</m:r></span></span></m:sub></m:ssub><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>-</m:r><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>x</m:r></span></span></m:e></m:d><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>˄</m:r><m:r><i>u</i></m:r><m:r><i>)</i></m:r></span></span></m:omath><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">&nbsp;convergences to zero, weakly, whenever </span></span><m:omath><i><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r>u</m:r><m:r>&isin;</m:r></span></span></i><m:ssub><m:ssubpr><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><span style="font-style:italic"><m:ctrlpr></m:ctrlpr></span></span></span></m:ssubpr><m:e><i><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r>E</m:r></span></span></i></m:e><m:sub><i><span style="font-size:10.0pt"><span cambria="" math="" style="font-family:"><m:r>+</m:r></span></span></i></m:sub></m:ssub></m:omath><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">. In this note, we further investigate unbounded absolute weak convergence in E. We show that this convergence is stable under passing to and&nbsp;&nbsp; from ideals and sublattices. Compatible with un-convergenc, we show that uaw-convergence is topological, which means that E with uaw-topology forms a topological vector space. We consider some closedness properties for this type of convergence. Some examples&nbsp; are given to make the context more understandable. Finally, we introduce the notion of strongly continuous operators between Banach lattices and investigate some properties about them. Specially, we characterize Banach lattices with a strong unit in tems of this type of operators. </span></span></span></span></span></span><br> <span style="font-size:11pt"><span style="line-height:22.0pt"><span style="text-autospace:none"><span style="font-family:Calibri,sans-serif"><b><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">Material and methods</span></span></b></span></span></span></span><br> <span style="font-size:11pt"><span style="line-height:22.0pt"><span style="text-autospace:none"><span style="font-family:Calibri,sans-serif"><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">In this paper, we combine the order structure and the norm structure in a Banach lattice to consider the unbounded convergences in the category of all Banach lattices. </span></span></span></span></span></span><br> <span style="font-size:11pt"><span style="line-height:22.0pt"><span style="text-autospace:none"><span style="font-family:Calibri,sans-serif"><b><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">Results and discussion</span></span></b></span></span></span></span><br> <span style="font-size:11pt"><span style="line-height:22.0pt"><span style="text-autospace:none"><span style="font-family:Calibri,sans-serif"><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">We shall show the following main results.</span></span></span></span></span></span><br> <span style="font-size:11pt"><span style="line-height:22.0pt"><span style="text-autospace:none"><span style="font-family:Calibri,sans-serif"><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">1. The uaw-convergence in a Banach lattice is topological.</span></span></span></span></span></span><br> <span style="font-size:11pt"><span style="line-height:22.0pt"><span style="text-autospace:none"><span style="font-family:Calibri,sans-serif"><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">2. In an order continuous Banach lattice, uaw-convergence is stable under passing to and from sublattices and ideals.</span></span></span></span></span></span><br> <span style="font-size:11pt"><span style="line-height:22.0pt"><span style="text-autospace:none"><span style="font-family:Calibri,sans-serif"><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">3. Introduce strongly continuous operators between Banach lattices and investigate some properties of them. </span></span></span></span></span></span><br> <span style="font-size:11pt"><span style="line-height:22.0pt"><span style="font-family:Calibri,sans-serif"><b><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">Conclusion</span></span></b></span></span></span><br> <span style="line-height:22.0pt"><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">The following main conclusions were drawn from this research.</span></span></span><br> <span style="line-height:22.0pt"><span style="font-size:10.0pt"><span new="" roman="" style="font-family:" times="">Theorem 2. Theorem 4.&nbsp; Proposition 10. Theorem 11.</span></span></span><br> &nbsp; همگرایی ضعیف مطلق غیر کراندار, ایده ال, زیر مشبکه, بسته بودن, عملگر پیوسته قوی. Unbounded absolute weak convergence, ideal, sublattice, closedness, unbounded norm convergence, strongly continuous operator. 129 137 http://mmr.khu.ac.ir/browse.php?a_code=A-10-435-4&slc_lang=fa&sid=1 Omid Zabeti امید ضابطی o.zabeti@gmail.com 10031947532846005470 10031947532846005470 Yes University of Sistan and Baluchestan دانشگاه سیستان و بلوچستان