پديد آورنده :
دهقاني مديسه، حسين
عنوان :
جواب هاي مثبت براي معادلات عملگري AXB=C
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد راهنما :
فريد بهرامي
استاد مشاور :
محمود منجگاني
واژه نامه :
به فارسي و انگليسي
توصيفگر ها :
معكوس تعميم يافته , معكوس مور - پنروز
تاريخ نمايه سازي :
1394/09/15
استاد داور :
رسول نصراصفهاني، مهدي نعمتي
تاريخ ورود اطلاعات :
1396/10/05
چكيده انگليسي :
Positive solutions to operator equations AXB C Hossein Dehghani Madiseh hossein dehghani@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Farid Bahrami fbahrami@cc iut ac ir Advisor Dr Seyed Mahmoud Manjegani manjgani@cc iut ac ir 2010 MSC 47A62 47A05 Keywords Operator equation Positive solution Generalized inverses Abstract The operator eqution 1 AXB Chas been studied by several authors but under the extra condition that the operators A and B haveclosed ranges In this thesis we present di erent results regarding the existence of solution and alsothe existence of positive solution to AXB C without this extra hypothesis The main goal of this thesis is to study the operator equation 1 where A B and C are boundedlinear operators de ned on convenient Hilbert spaces This kind of equation has been studied byseveral authors because of its multiple applications in di erent areas as for example control theoryand sampling The reader is referred to 6 11 18 and the references therein However in these worksit is only considered the case in which A B and C are matrices or have closed range Our goal isto study equation 1 with arbitrary operators A B and C This consideration implies that someclassical results are not longer valid For instance it is well known that if A and B have closed rangethen the equation 1 is solvable i e there exists a bounded linear operator D such that ADB C ifand only if AA CB B C for every inner inverses A and B of A and B respectively Recall thatA non necessarily bounded is an inner inverse of A if AA A A However it is easy to see that thisresult fails if A B have not closed range In fact for every operator A it holds AA AA A A butAXA A is solvable if and only if A has closed range 14 Therefore our rst aim is to determine
استاد راهنما :
فريد بهرامي
استاد مشاور :
محمود منجگاني
استاد داور :
رسول نصراصفهاني، مهدي نعمتي
