آرنز منظم نگاشت های دو خطی کران دار

Abstract

در این مقاله به خواص آرنز منظم نگاشت دو خطی کران­دار می­پردازیم و نشان می­دهیم که نگاشت دو خطی کران­دار آرنز منظم است اگر و تنها اگر نگاشت خطی با ضابطۀ ضعیف فشرده باشد. سپس قضیه‌ای را اثبات می­کنیم که ویژگی ضعیف فشردگی نگاشت دو خطی کران­دار و آرنز منظم را به یک‌دیگر مرتبط می­سازد. هم‌چنین به بررسی آرنز منظم و خاصیت ضعیف فشردگی نگاشت­های خطی کران­دار می­پردازیم و نتایجی مشابه نتایج دیلز، اولگر و آریکان را بیان می­کنیم. در ادامه ارتباط بین آرنز منظم جبرهای باناخ و انعکاسی بودن را بررسی می‌کنیم

Full text


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   
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                
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Haghnejad@uma.ac.ir
1
.Bounded bilinear mapping
2
. R. E. Arens
3
. Arens product
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       
   
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

            


                  

     



     

    
        




    
            
    
 



 
         


  


   


     
          
       
    [10] 
     
 
  

   
   


      

1
.A. 
lger
2
. Weakly compact
3
. Adjoint
4
. Flip map
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
     




     

  


   

      
 
  
 
     
 
  


     


    
  


      





     


 
  


  

  
   
    
  
       
 
     
    
 
     
 
 
  
 
  
1
. Approximately unital
2
. Unital
Downloaded from mmr.khu.ac.ir at 0:21 IRDT on Friday September 18th 2020



 
 

 
 


 




 
 
  

     











     


          
   



                 
                   
 


  
  

    



 

   

    

    


     

   


    
    
 
     
   
       
    

           
      
1
. N. Arikan
Downloaded from mmr.khu.ac.ir at 0:21 IRDT on Friday September 18th 2020


       
        


 
          

  


   
   
   





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 

 

             

  








  

  
  


  
  

           
   
     
  


  


  
  
 
  

          
  
   
   
 
    
  
 
      
    
1
. H. G. Dales
2
. A. Rodrigues-Palacios
3
. M. V. Velasco
Downloaded from mmr.khu.ac.ir at 0:21 IRDT on Friday September 18th 2020



   

  

  
  
  






          

 
 
 


 



 
 

 
 
   
   



.  
           


           



  

  
  

      
        
  
 

         
 
     
     
 

     

    
 

     
    
   








   
 
     
1
. A. T. Lau
Downloaded from mmr.khu.ac.ir at 0:21 IRDT on Friday September 18th 2020



 



    

  





     


     





   
       
    
 
  

        
          
    
  
        
  
  









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
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lger A., "Topological center of certain dual algebras", Trans. Amer. Math. Soc.
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lger A., "Weakly compact bilinear forms and Arens regularity", Proc. Amer. Math. Soc.
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