1、1?D‰?mSK21.?3?5?mX?ldv￡C5?q5=d(xzyz)=d(xy)d(αxαy)=|α|d(xy).?x?=d(x0).y(X??)D‰?5?m.2.?(X??)D‰?5?muxy∈Xd(xy)=???0x=y?x?y?1x?=y.ydl?d‰p??l=?3X?‰??1?d(xy)=?x?y?1xy∈X.3.?XLES?x=(x1x2)??N?x?=∞?n=12?nmin(1|xn|).(1)??X?‰(2)?x?y?

2、??X?lbe?`?x(n)?x?→0(n→∞)?.4.3C1[ab]?x?1=(?ba(|x(t)|2|x?(t)|2)dt)12?x∈C1[ab].(1)y??1C1[ab]?‰(2)(C1[ab]??1)??5.3Cn‰?x?=maxi|xi|yBanach?m.6.?X[01]kYx=x(t)?8.y?x?=(?10|x(t)|2dt)12X?‰?X3‰e??.7.?(X??)D‰?mX?=0.yX?Banach?m??^?X?

3、?S=x∈X???x?=1???.1317.y?5?mX?x8??E8x0∈X8A￡0x0???8Ax0=yx0|y∈AE8.18.?M?5?mX?f8yC0(A)=α1x1αnxn∈X|ngxk∈Aαk≥0…n?k=1αk=1.19.?C(01]L(01]Y…k.?x(t)??N.?x?=sup|x(t)||0t≤1.y(1)??C(01]?m?‰(2)l∞?C(01]???f?m??.20.?X?n‘D‰?5?mE0X?4f?my?

4、3x0∈X??x0?=1d(x0E0)=infx∈E0?x0?x?=1.21.3L2[01]5‰:?f?1=?10|f(t)|dt?f?2=(?10|f(t)|2dt)12?f?3=(?10(1t)|f(t)|2dt)12.=??d‰`nd.22.?xnBanach?mX?:?.e?3(0∞)?K4~??g(t)??xn?≤g(n)(n=123).y?∞n=1xn.23.?(X??)D‰?mYX?f?mux∈Xδ=d(xY)=infy∈

5、Y?x?y?.XJ?3y0∈Y??x?y0?=δ?y0x??Z%C.(1)yXJYX?k?‘f?m.Kz?x∈X?3?Z%C.(2)~`?Yk?‘?m?(1)?(.(3)~`???Z%C??.(4)yuz?:x∈Xxuf?mY??Z%C:88.24.?(Xk??k)??D‰?mx=xkxk∈Xk(k=12)…v^??∞k=1?xk?pk∞^XLkx??N.U?I?5$????5?m3X?x?=(∞?k=1?xk?pk)1p(p≥1).y