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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>;<br/>

<a NAME="E1:72"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="clopban1.html#K14" title="CLOPBAN1:func.14">C_NormSpace_of_BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span><br/> for <font color="Olive" title="b3">c</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a> holds <br/> ( ( <span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 implies <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <span class="p1">(<span class="default"><a href="clopban1.html#K14" title="CLOPBAN1:func.14">C_NormSpace_of_BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> ) &amp; ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <span class="p1">(<span class="default"><a href="clopban1.html#K14" title="CLOPBAN1:func.14">C_NormSpace_of_BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span> implies <span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 ) &amp; <span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">c</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b1">x</font></span>)</span></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><font color="Olive" title="b3">c</font></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span> &amp; <span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Olive" title="b2">y</font></span>)</span></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1"><a href="clvect_1.html#K5" title="CLVECT_1:func.5">||.</a><span class="default"><font color="Olive" title="b2">y</font></span><a href="clvect_1.html#K5" title="CLVECT_1:func.5">.||</a></span> )
 
<b>by </b><i><a class="ref" href="clopban1.html#T41" target="_self" title="CLOPBAN1:th.41">Th41</a></i>;<br/>
<b>hence </b><a NAME="E2:72"/>
 <a href="clopban1.html#K14" title="CLOPBAN1:func.14">C_NormSpace_of_BoundedLinearOperators</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> is <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">ComplexNormSpace-like</a>
 <b>by </b><i><a class="ref" href="clvect_1.html#D10" title="CLVECT_1:def.10">CLVECT_1:def 10</a></i>;<br/>


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