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6. If M, = N(T)={x|Tx=0} in Prob. 4, show that %3D (a) T*(H,)c M,+, (b) [T(H,)}†c N(T*), (c) M,=[T*(H2)]*.

6. If M, = N(T)={x|Tx=0} in Prob. 4, show that %3D (a) T*(H,)c M,+, (b) [T(H,)}†c N(T*), (c) M,=[T*(H2)]*.

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Solve only Question no.06 (Question 4 i uploaded for hint & help to solve Question 6).

4. Let H¡ and H, be Hilbert spaces and T: Hj→H, a bounded linear operator. If M,cH, and M2<H2 are such that T(M,)c M2, show that M,>T*(M,+). |
Transcribed Image Text:4. Let H¡ and H, be Hilbert spaces and T: Hj→H, a bounded linear operator. If M,cH, and M2<H2 are such that T(M,)c M2, show that M,>T*(M,+). |
6. If M, = N(T)={x|Tx=0} in Prob. 4, show that (a) T*(H,)< M,+, (b) [T(H,)}†c N(T*), (c) M,=[T*(H,)]}.
Transcribed Image Text:6. If M, = N(T)={x|Tx=0} in Prob. 4, show that (a) T*(H,)< M,+, (b) [T(H,)}†c N(T*), (c) M,=[T*(H,)]}.
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