2-Absolutely Summing Operators on the Space C(T, X)

✍ Scribed by Dumitru Popa

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 763 KB
• Volume: 239
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1999.6440

✦ Synopsis

We give for some Banach spaces X and Y examples of linear and continuous operators U : C ( T , X ) + Y , such that U' cp E As,(X, Y ) , for each cp E C ( T ) and U # : C ( T ) + As,(X,Y) is a 2-absolutely summing operator with respect to the 2-absolute norm on As,(X, Y ) , but U is not 2-absolutely summing. o 1999 Aca deniic Press For X a Banach space, 1 I r I a, and ( x , , ) ~ c X we write wr(xn I n E N ) = sup{(C:=lIx*(x,,)I ) Ix* E X*, Ilx*ll I 11, if r < a and wx(xn I n E N ) = ~~p , ~~~l l x ~l l , if r = m, w,(X> = { ( x , ~> ~~~