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<b>let </b><font color="Maroon">X</font> be   <a href="clvect_1.html#NM5">ComplexNormSpace</a>, <font color="Maroon">Y</font> be   <a href="clvect_1.html#NM5">ComplexNormSpace</a>;<br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  =  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="clopban1.html#K12" target="_self">PreNorms</a> <span class="p2">(<span class="default"><a href="clopban1.html#K11" target="_self">modetrans</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span></span>)</span>;<br/>
<a NAME="E1:58"/><i><font color="Green">E38</font></i>: 
for <font color="Olive">z</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">z</font> <a href="hidden.html#R2">in</a>  <a href="clopban1.html#K8" target="_self">BoundedLinearOperators</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">z</font>) <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a> 
 
;<br/>
<a NAME="E2:58"/>
 ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="clopban1.html#K8" target="_self">BoundedLinearOperators</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>, <a href="numbers.html#K1">REAL</a>  st <br/>for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="clopban1.html#K8" target="_self">BoundedLinearOperators</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> holds <br/><font color="Olive">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">x</font>)
 
<b>from </b><i><a class="ref" href="funct_2.html#S2">FUNCT_2:sch 2</a>(<a class="txt" href="clopban1.html#E1:58"><i><font color="Green">E38</font></i></a>);<br/></i>
<b>hence </b><a NAME="E3:58"/>
 ex <font color="Olive">NORM</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="clopban1.html#K8" target="_self">BoundedLinearOperators</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>, <a href="numbers.html#K1">REAL</a>  st <br/>for <font color="Olive">f</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="clopban1.html#K8" target="_self">BoundedLinearOperators</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> holds <br/><font color="Olive">NORM</font> <a href="seq_1.html#K2">.</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="clopban1.html#K12" target="_self">PreNorms</a> <span class="p2">(<span class="default"><a href="clopban1.html#K11" target="_self">modetrans</a> <font color="Olive">f</font>,<font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span></span>)</span>
 ;<br/>


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