Let X := {(a
): summation|a| < infinity{ be the space of absolutely convergent
sequences. Define the? l1 and l(infinity) metrics on this space by
d(l1)(a, b) := summation |a - b|
where n=0 at first and goes to n = infinity.
d(l(infinity))(a, b) := sup|a - b|
I hope this is clear if not let me know. Show that there exist sequences x(of elements of X which are convergent with respect to the d(l(infinity)) metric but not with respect to the d(l1) metric
): summation|a| < infinity{ be the space of absolutely convergentsequences. Define the? l1 and l(infinity) metrics on this space by
d(l1)(a
, b) := summation |a - b|where n=0 at first and goes to n = infinity.
d(l(infinity))(a
, b) := sup|a - b|I hope this is clear if not let me know. Show that there exist sequences x(of elements of X which are convergent with respect to the d(l(infinity)) metric but not with respect to the d(l1) metric