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The Three Space Problem and Ideals of Operators

✍ Scribed by Hans Jarchow

Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
553 KB
Volume
119
Category
Article
ISSN
0025-584X

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✦ Synopsis

1. Int,rodrietion

\Ve will be concerned with a particular aspect of the following quest'ion which Consider a weak CAUCHY sequence (zJ in X , and let z be its limit in [X**. o(X**, X * ) ] . If Q : X + X / Y is the quotient map, then (Qx,) converges weakly in S I P since XI1is wsc. Hence &**zEX/Y and Q**x=Qx for some X E X . Note that z -x belongs to Y**. Moreover. certain convex combinations of the Q (r -xN) form a null sequence in the BANACH space X / Y . Let A k c N be finite and Q 2 0 such that max A,<rnin A,,,, ai= 1, andjl&(z,-x)((<k-i, where z,:= ujxj, i E A ,

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