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1、1lù1nÙk.5f1001001lù1nÙk.5f§1.k.5fk.5¼1001lù1nÙk.5f§1.k.5fk.5¼½½½ÂÂÂ1.1.X,X1Dm§T:X→X15N§e3~êM≥0¦1001lù1nÙk.5f§1.k.5fk.5¼½½½ÂÂÂ1.1.X,X1Dm§T:X→X15N§e3~êM≥0¦kTxk≤Mkxk,∀x∈XK¡T´k."1001lù1nÙk.5f§1.k.5fk.5¼½½½ÂÂÂ1.1.X,X1Dm§T:X→X15N§e3~êM≥0¦kTxk≤Mkxk,∀x∈XK¡T´k."5µT´k.⇐⇒T
2、rX¥k.8NX1¥k.8⇐⇒TrX,r¥B(θ,r)NX1¥k.8(r>0)"1001lù1nÙk.5f§1.k.5fk.5¼½½½ÂÂÂ1.1.X,X1Dm§T:X→X15N§e3~êM≥0¦kTxk≤Mkxk,∀x∈XK¡T´k."5µT´k.⇐⇒TrX¥k.8NX1¥k.8⇐⇒TrX,r¥B(θ,r)NX1¥k.8(r>0)"5fü:ëY5NëY51001lù1nÙk.5f§1.k.5fk.5¼½½½ÂÂÂ1.1.X,X1Dm§T:X→X15N§e3~êM≥0¦kTxk≤Mkxk,∀x∈XK¡T´k
3、."5µT´k.⇐⇒TrX¥k.8NX1¥k.8⇐⇒TrX,r¥B(θ,r)NX1¥k.8(r>0)"5fü:ëY5NëY5101½½½nnn1.1.T:X→X15§KT3XþëY⇐⇒T3,:x0∈XëY"101½½½nnn1.1.T:X→X15§KT3XþëY⇐⇒T3,:x0∈XëY"yyy²²²/=⇒0Ü©w,§=y/⇐=0Ü©101½½½nnn1.1.T:X→X15§KT3XþëY⇐⇒T3,:x0∈XëY"yyy²²²/=⇒0Ü©w,§=y/⇐=0Ü©T3,:x0ëY§é?¿x∈X9?¿xn→xk(x0+xn−x
4、)→x0,∴T(x0+xn−x)→T(x0),101½½½nnn1.1.T:X→X15§KT3XþëY⇐⇒T3,:x0∈XëY"yyy²²²/=⇒0Ü©w,§=y/⇐=0Ü©T3,:x0ëY§é?¿x∈X9?¿xn→xk(x0+xn−x)→x0,∴T(x0+xn−x)→T(x0),dT5,=T(x0)+T(xn)−T(x)→T(x0)§¤±T(xn)→T(x),∴T3x:ëY"101½½½nnn1.1.T:X→X15§KT3XþëY⇐⇒T3,:x0∈XëY"yyy²²²/=⇒0Ü©w,§=y/⇐=0Ü©T3,:x0ëY§é?¿x∈X9
5、?¿xn→xk(x0+xn−x)→x0,∴T(x0+xn−x)→T(x0),dT5,=T(x0)+T(xn)−T(x)→T(x0)§¤±T(xn)→T(x),∴T3x:ëY"líÑT3XþëY"101½½½nnn1.1.T:X→X15§KT3XþëY⇐⇒T3,:x0∈XëY"yyy²²²/=⇒0Ü©w,§=y/⇐=0Ü©T3,:x0ëY§é?¿x∈X9?¿xn→xk(x0+xn−x)→x0,∴T(x0+xn−x)→T(x0),dT5,=T(x0)+T(xn)−T(x)→T(x0)§¤±T(xn)→T(x),∴T3x:ëY"líÑT3Xþ
6、ëY"5fk.5ëY5kÛ'XQº101½½½nnn1.1.T:X→X15§KT3XþëY⇐⇒T3,:x0∈XëY"yyy²²²/=⇒0Ü©w,§=y/⇐=0Ü©T3,:x0ëY§é?¿x∈X9?¿xn→xk(x0+xn−x)→x0,∴T(x0+xn−x)→T(x0),dT5,=T(x0)+T(xn)−T(x)→T(x0)§¤±T(xn)→T(x),∴T3x:ëY"líÑT3XþëY"5fk.5ëY5kÛ'XQº½½½nnn1.2.T:X→X15§KTëY⇐⇒Tk."101½½½nnn1.1.T:X→X15§KT3XþëY⇐⇒
7、T3,:x0∈XëY"yyy²²²/=⇒0Ü©w,§=y/⇐=0Ü©T3,:x0ëY§é?¿x∈X9?¿xn→xk(x0+xn−x)→x0,∴T(x0+xn−x)→T(x0),dT5,=T(x0)+T(xn)−T(x)→T(x0)§¤±T(xn)→T(x),∴T3x:ëY"líÑT3XþëY"5fk.5ëY5kÛ'XQº½½½nnn1.2.T:X→X15§KTëY⇐⇒Tk."yyy²²²=⇒TëY§KT3θ:ëY§3δ>0¦kx−θk≤δkkTxk=kTx−Tθk≤1"101TrXδ¥B(θ,δ)NX1¥k.8§Tk."10
8、1TrXδ¥B(θ,δ)NX1¥k.8§Tk."⇐=Tk.§3M≥0¦kTxk≤Mkxk,∀x∈X§dd§x→θkTx→θ=Tθ§101TrXδ¥B(θ
