ISSN 2234-8417 (Online) ISSN 1598-5857 (Print)

 
 
 
   
 
Table of Contents
   
 
2014's   32,3-4(May)
   
 
  Compact interpolation on $AX=Y$ in Alg$\mathcal{L}
    By Joo Ho Kang ..........1520
   
 
 
Generic Number - 1520
References - 0
Written Date - May 16th, 14
Modified Date - May 16th, 14
Downloaded Counts - 52
Visited Counts - 370
 
Original File
 
Summary
In this paper the following is proved: Let $\mathcal{L}$ be a subspace
lattice on a Hilbert space $\mathcal{H}$ and X and Y be operators acting on
$\mathcal{H}$. Then
there exists a compact operator A in Alg$\mathcal{L}$ such that AX = Y if and only
if
$\sup \left\{ {\norm{E^\perp Y f} \over \norm{E^\perp X f}} : f \in
\mathcal{H}, ~E \in \mathcal{L}
\right\} = K < \infty$ and $Y$ is compact. Moreover,
if the necessary condition holds, then we may choose an operator $A$ such
that $AX = Y$ and $\norm{A} = K$.
 
 
   
 
   

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