數(shù)學(xué)專業(yè)畢業(yè)論文希爾伯特空間中子空間的閉性與補(bǔ)性黃雪梅-展示頁(yè)
2025-01-25 16:57本頁(yè)面
【正文】 b space, then not necessarily had been established. KeyWord: Inner product space。希爾伯特空間中子空間的閉性與補(bǔ)性黃雪梅(孝感學(xué)院數(shù)學(xué)系031114112)摘要：本文主要討論了內(nèi)積空間中子空間所需的條件,并證明了以下主要結(jié)果：（1） 設(shè)是內(nèi)積空間,是中的子空間，則的子空間,使得.（2） 若是內(nèi)積空間,是中的有限維子空間,則。設(shè)是無(wú)限維內(nèi)積空間,是中的無(wú)限維子空間,則不一定成立．關(guān)鍵詞：內(nèi)積空間；直交補(bǔ)；子空間；閉集. Hilbert space neutron closed space with the plementary natureHuang xuemei(031114112,Department of Mathematics,Xiaogan University)Abstract: This article mainly discussed the inner product space neutron space to satisfy the condition which needed, and has proven belowthe main result: (1)supposes is the inner product space, is center sub space, then when also only when has sub space, causes .(2)if is the inner product space, is center finiteDimensional the sub space, then establishment。 Is perpendicular to makes up。 Closedset.0 問題的提出在文獻(xiàn)[1]中提出了如下問題：“Let be a space, is a subset of ,then is a closed the is closed,every vector in can be deposed into ,where is in .If is also a subspace，can we conclude that ? why?
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