Let V a norma space with 2 norms , lets say norm 1 and norm 2

Show that the function identity es continuos iff the set

A is bounded with norm 2

Please somebody give me a biiiiiiiiiiiiig hint....

Regards...

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- May 23rd 2011, 07:52 PMorbitContinuity and norm space
Let V a norma space with 2 norms , lets say norm 1 and norm 2

Show that the function identity es continuos iff the set

A is bounded with norm 2

Please somebody give me a biiiiiiiiiiiiig hint....

Regards... - May 23rd 2011, 09:18 PMDrexel28
Come on man--you really need to show some effort. You need remember that linear operators are continuous if and only if they're bounded. So, will be bounded if and only if there is a constant such that for all ... now why is this equivalent to saying that this inequality holds true for every ?

- May 24th 2011, 04:36 PMorbit
- May 24th 2011, 09:35 PMDrexel28
- May 25th 2011, 01:16 PMorbit
- May 25th 2011, 02:33 PMDrexel28