I need to show that a linear functional on a Hilbert space defined by has operator norm . I have already shown by the Cauchy Schwarz inequality that . I think now I need to show that . Any help would be great, Thanks
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Originally Posted by ejgmath I need to show that a linear functional on a Hilbert space defined by has operator norm . I have already shown by the Cauchy Schwarz inequality that . I think now I need to show that . Any help would be great, Thanks Tip, plug in .
Into where, can you elabourate?
Originally Posted by ejgmath Into where, can you elabourate? Into . What you want is for some x with , which precisely shows the inequality you are looking for (as ).
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