Dear Colleagues,

I have a problem in the attachment and could you please help me in solving it.

Best Regards.

Raed.

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- May 2nd 2011, 04:45 AMraedHahn-Banach Theorem (Normed Spaces)
Dear Colleagues,

I have a problem in the attachment and could you please help me in solving it.

Best Regards.

Raed. - May 2nd 2011, 08:20 AMOpalg
Since is an inner-product space, every linear functional is given by an inner product. In fact, if then the functional is given by . Use that fact to show that .

Now that you know , you have to figure out how to extend f to a linear functional on without increasing the norm. - May 2nd 2011, 10:36 AMraed
Thank you very much for your reply I have already proved the norm of f. But the problem is in finding a linear extension of f that preserves the norm.

Best Regards. - May 2nd 2011, 12:04 PMOpalg