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Este Cmap, tiene información relacionada con: Espacio B(N,N'), OPERADORES LINEALES ACOTADOS a partir de la cota definimos su NORMA, Β(N,N') está compuesto por los OPERADORES LINEALES CONTINUOS T:N→N', NORMA definida por <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfenced open="‖" close="‖"> <mtext> T </mtext> </mfenced> <mtext> =sup </mtext> <mfenced open="{" close="}"> <mfenced open="‖" close="‖"> <mtext> T(x) </mtext> </mfenced> <mtext> : </mtext> <mfenced open="‖" close="‖"> <mtext> x </mtext> </mfenced> <mtext> ≤1 </mtext> </mfenced> </mrow> </math>, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfenced open="‖" close="‖"> <mtext> T </mtext> </mfenced> <mtext> =sup </mtext> <mfenced open="{" close="}"> <mfenced open="‖" close="‖"> <mtext> T(x) </mtext> </mfenced> <mtext> : </mtext> <mfenced open="‖" close="‖"> <mtext> x </mtext> </mfenced> <mtext> ≤1 </mtext> </mfenced> </mrow> </math> por Teo. 5.1.3 es equivalente a <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mfenced open="‖" close="‖"> <mtext> T </mtext> </mfenced> <mtext> =inf </mtext> <mfenced open="{" close="}"> <mtext> K: </mtext> <mfenced open="‖" close="‖"> <mtext> T(x) </mtext> </mfenced> <mtext> ≤K </mtext> <mfenced open="‖" close="‖"> <mtext> x </mtext> </mfenced> <mtext> , ∀x∈N </mtext> </mfenced> </mrow> </math>, Β(N,N') si N'=R o N'=C constituye el Espacio Dual N*, Espacio Dual N* sus elementos se llaman FUNCIONALES LINEALES CONTINUOS, Β(N,N') por Teorema 5.2.1 es Espacio Lineal Normado