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纰╁＋鐮旂┒鐢熷叆瀛�(xu茅)鑰冭│澶х侗
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浜�銆佽€冭│瑕佹眰
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锛堜簩锛塇ilbert 绌洪枔
1锛� 鍏�(n猫i)绌嶇┖闁撶殑瀹氱京锛屾€ц唱(zh矛)锛涘収(n猫i)绌嶈垏鑼冩暩(sh霉)銆佽窛闆箣闁撶殑闂�(gu膩n)绯�銆�
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4锛� Hilbert 绌洪枔鐨勫畾缇�锛汬ilbert 绌洪枔涓婄殑姝ｈ(gu墨)姝ｄ氦鍩�锛屾瑕�(gu墨)姝ｄ氦鍒嗚В锛�
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琛ㄧ従(xi脿n)瀹氱悊锛孒ilbert
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8锛� Hilbert 鍏辫粵绠楀瓙鐨勫畾缇�銆佹€ц唱(zh矛)鍙婂叾琛ㄧず锛涘彲鍒� Hilbert 绌洪枔涓婃湁鐣岀窔鎬х畻瀛愮殑鐭╅櫍琛ㄩ仈
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1. Banach 绌洪枔涓婄殑鏈夌晫绶氭€х畻瀛愬畾缇�锛涚畻瀛愯寖鏁�(sh霉)鐨勮▓绠�锛涜寖鏁�(sh霉)鐨勬瘮杓冦€�
2. 鏈夌晫绶氭€х畻瀛愮┖闁� ),( YXL 鐨勬€ц唱(zh矛)銆�
3. 绠楀瓙鐨勯€嗭紝閫嗙畻瀛愬瓨鍦�銆侀€ｇ簩(x霉)鐨勬浠讹紱鍒╃敤閫嗙畻瀛愯В姹轰竴浜涚⿳鍒嗘柟绋嬬瓑鏂归潰鐨勫闅涘晱椤�銆�
4. Hahn-Banach 瀹氱悊锛涙摯寮靛畾鐞嗙殑骞剧ó琛ㄧ従(xi脿n)褰㈠紡锛屽 Banach 鎿村嫉瀹氱悊銆丅ohnenblust-Sobczyk
瀹氱悊绛�銆�
5. Hahn-Banach 瀹氱悊鐨勪竴浜涙帹璜�锛岄珨鐝�(xi脿n)鐨勪笉鍚屽伌(c猫)闈㈢殑 Hahn-Banach 瀹氱悊鐨勫叿楂旇〃鐝�(xi脿n)褰㈠紡锛�
Hahn-Banach 瀹氱悊鐨勫咕浣曞舰寮�銆侶ahn-Banach 瀹氱悊鍦ㄧ悊璜栧強瀵﹂殯涓婄殑鎳�(y墨ng)鐢�銆�
6. 鍒嗛洟瀹氱悊锛屽強鍏惰垏 Hahn-Banach 瀹氱悊涔嬮枔鐨勯棞(gu膩n)绯�銆�
7. Baire 缍卞畾鐞�锛涚涓€缍遍泦銆佺浜岀侗闆嗙殑瀹氱京鑸囧垎椤�銆�
8. 涓€鑷存湁鐣屽師鐞嗭紙鍏遍炒瀹氱悊锛�锛涢枊鏄犲皠瀹氱悊锛汢anach 閫嗙畻瀛愬畾鐞嗭紱闁夊湒褰㈠畾鐞嗕互鍙婂畠鍊戠殑鎳�(y墨ng)
鐢�銆�
9. 灏嶅伓绌洪枔鐨勫畾缇�锛屽咕鍊嬪叿楂旂┖闁撲笂鐨勫皪鍋剁┖闁撳強瀹冨€戠殑閫ｇ簩(x霉)娉涘嚱褰㈠紡锛屽
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10. 浜屾灏嶅伓銆佸吀鍨嬫槧灏�銆佽嚜鍙嶇┖闁撶殑瀹氱京锛涙湁闄愮董璩﹁寖绶氭€х┖闁�銆� )1](,[ ??? pbaL
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Hilbert 绌洪枔鐨勮嚜鍙嶆€ц唱(zh矛)銆備簡瑙ｅ父瑕嬬殑涓嶆槸鑷弽绌洪枔鐨勪緥瀛愩€�
11. Banach 鍏辫粵绠楀瓙鐨勫畾缇�銆佹€ц唱(zh矛)鍙婂叾鐭╅櫍琛ㄧず銆�
12. 绠楀瓙鐨勫€煎煙銆侀浂绌洪枔銆佸晢绌洪枔鐨勫畾缇╄垏瀹冨€戜箣闁撶殑闂�(gu膩n)绯�銆�
锛堝洓锛夋湁鐣岀窔鎬х畻瀛愯瓬璜�
1. 鏈夌晫绶氭€х畻瀛愮殑闋�(y霉)瑙ｅ紡鑸囪瓬鐨勫畾缇╁強鍏惰▓绠�銆�
2. 鎺屾彙璀滃崐寰戝叕寮忥紝鎳�(y墨ng)鐢ㄥ叕寮忚В姹哄晱椤屻€�
3. 灏勫奖绠楀瓙鐨勫畾缇�锛涙湁鐣岀窔鎬х畻瀛愮殑涓嶈畩瀛愮┖闁撹垏绱勫寲瀛愮┖闁�锛汧.Riesz 绌洪枔鍒嗚В瀹氱悊銆�
4. 绶婄畻瀛愮殑瀹氱京鍙婂叾鎬ц唱(zh矛)锛涚穵绠楀瓙鐨勫渚�锛涚穵绠楀瓙鑸囩悊鎯崇殑闂�(gu膩n)绯�銆�
5. Riesz-Schauder 鐞嗚珫锛欶.Riesz 瀹氱悊锛涘叐鎿囦竴瀹氱悊锛汧redholm 浜ゆ浛瀹氱悊绛夊畾鐞嗗収(n猫i)瀹硅垏鎳�(y墨ng)
鐢�銆�
6. 鏈夌晫鑷即绠楀瓙鐨勫熀鏈€ц唱(zh矛)锛涚穵鑷即绠楀瓙鐨勫畾缇╄垏鎬ц唱(zh矛)锛涢厜绠楀瓙鐨勫畾缇╄垏鎬ц唱(zh矛)銆�
7. 鏈夌晫鑷即绠楀瓙鐨勮瓬娓害锛岃瓬鍒嗚В瀹氱悊鑸囧嚱鏁�(sh霉)婕旂畻銆�
鍏嶈铂(z茅)鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�(lu貌)锛屽鏈変镜鐘紝璜嬭伅(li谩n)绯绘垜鍊戠珛鍗冲埅闄�锛屽彟锛氭湰鏂囧儏浠ｈ〃浣滆€呭€嬩汉瑙€榛烇紝鑸囨湰缍�(w菐ng)绔欑劇闂�(gu膩n)銆傚叾鍘熷壍(chu脿ng)鎬т互鍙婃枃涓櫝杩版枃瀛楀拰鍏�(n猫i)瀹规湭缍�(j墨ng)鏈珯璀夊锛屽皪鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹广€佹枃瀛楃殑鐪熷鎬�銆佸畬鏁存€�銆佸強鏅傛€ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛璁€鑰呭儏浣滃弮鑰�锛屽苟璜嬭嚜琛屾牳瀵︾浉闂�(gu膩n)鍏�(n猫i)瀹�銆�
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鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
