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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being <a href="clopban1.html#V3" title="CLOPBAN1:attr.3">bounded</a> <a href="clopban1.html#NM1" title="CLOPBAN1:NM.1">LinearOperator</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> holds  <span class="p1">(<span class="default"><a href="clopban1.html#K13" title="CLOPBAN1:func.13">BoundedLinearOperatorsNorm</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="clopban1.html#K12" title="CLOPBAN1:func.12">PreNorms</a> <font color="Olive" title="b1">f</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">f</font> be  <a href="clopban1.html#V3" title="CLOPBAN1:attr.3">bounded</a> <a href="clopban1.html#NM1" title="CLOPBAN1:NM.1">LinearOperator</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="clopban1.html#K13" title="CLOPBAN1:func.13">BoundedLinearOperatorsNorm</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="clopban1.html#K12" title="CLOPBAN1:func.12">PreNorms</a> <font color="Maroon" title="c3">f</font></span>)</span></span><br/>



<a NAME="E1:58"/><i><font color="Green" title="E37">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="clopban1.html#K8" title="CLOPBAN1:func.8">BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="ref" href="clopban1.html#D8" target="_self" title="CLOPBAN1:def.8">Def8</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">f'</font> = <font color="Maroon" title="c3">f</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="clopban1.html#K13" title="CLOPBAN1:func.13">BoundedLinearOperatorsNorm</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">f</font> = 
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="clopban1.html#K12" title="CLOPBAN1:func.12">PreNorms</a> <span class="p2">(<span class="default"><a href="clopban1.html#K11" title="CLOPBAN1:func.11">modetrans</a> <font color="Maroon" title="c4">f'</font>,<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="clopban1.html#E1:58"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="clopban1.html#D12" target="_self" title="CLOPBAN1:def.12">Def12</a></i>
<br/>.= 
 <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <span class="p1">(<span class="default"><a href="clopban1.html#K12" title="CLOPBAN1:func.12">PreNorms</a> <font color="Maroon" title="c3">f</font></span>)</span>
<b>by </b><i><a class="ref" href="clopban1.html#T33" target="_self" title="CLOPBAN1:th.33">Th33</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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