پديد آورنده :
ركن آباد، مژگان
عنوان :
عملگرهاي تركيبي وزن دار روي فضاهاي لبگ
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي محض ، آناليز
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد راهنما :
رسول نصر اصفهاني
استاد مشاور :
حسين جوانشيري
واژه نامه :
به فارسي و انگليسي
توصيفگر ها :
كران داري , معكوس پذيري , فشردگي , صعود , نزول
تاريخ نمايه سازي :
1394/11/11
استاد داور :
مهدي نعمتي، سيما سلطاني
چكيده انگليسي :
Weighted composition operators on Lebesgue spaces MOJGAN ROKNABADI m roknabadi@math iut ac ir January 2016 A Thesis for the Degree of Master of Philosophy in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Professor Rasoul Nasr Isfahani isfahani@cc iut ac irAdvisor Dr Hossien Javanshiri h javanshiri@yazd ac ir2000 MSC 47B05 47B38Key Words Weighed composition operator Boundedness Closedness of range In vertibility Compactness Ascent Descent Lebesgue spaceAbstract In this thesis we an expanded account on Lp spaces according some works by Takagi 1992 and Kumar 2008 Let pX q and pY q be finite and complete measur spaces and 1 p 8 The setcosisting of all measurable function f on X with f Lp p q 8 froms Lp pX q space whichis a Banach space under the norm Lp p q Let u Y C be a measurable function and let Y X be a non singular measurabletransformation that is apoint mapping from Y into X such that 1 pEq P for every E P With such u and we now define a weighted composition operator uC from Lp p q into thelinear space of all measurable functions on Y by pf P Lp p q y P Y q uC pf qpyq upyqf p pyqq For 1 p q 8 we investigate properties of these operators between Lp spaces bounded ness closedness of ranges invertibility compactness ascent and descent We first show thatuC is bounded if and only if hEp u p q 1 is in L8 p q in this case there is c 0 such that u p d c pEq pE P q 1 pEqand # uC p inf u p d c pEq c 0 f or any E P 1 pEq Also we show the bounded operator uC has closed range if and only if uC has finite rank Weprove that is if pX q is non atomic and uC Lp p q Lp p q a bounded operator then thenullity of uC is either zero or infinite By defining injective and surjective weighted compo sition operators we get invertible weighted composition operators In addition to offering twoexamples show that even if u 0 a e on Y the invertibility of in general does not guaranteeuC is invertible and vice versa
استاد راهنما :
رسول نصر اصفهاني
استاد مشاور :
حسين جوانشيري
استاد داور :
مهدي نعمتي، سيما سلطاني
