super weakly compact (operator)

Last-modified: 2010-07-31 (土) 12:09:44

Definition

  • Let X and Y be Banach spaces. An operator K in B(X,Y) is said to be super weakly compact if for all number e>0 there exists a positive integer n for which there do not exist finite sets imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c%7bx_1%2c%5cldots%2cx_n%5c%7d%20%5cmbox%7b%20in%20%7dS_X%5cmbox%7b%20and%20%7d%5c%7bf_1%5cldots%2cf_n%5c%7d%5cmbox%7b%20in%20%7dS_%7bX%5e*%7d%5c%5d%7d%25.png for which imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20f_j%28Kx_i%29%3ee%5cmbox%7b%20for%20%7d1%5cleq%20j%5cleq%20i%5cleq%20n%2c%20%5cmbox%7b%20and%20%7df_j%28Kx_i%29=0%5cmbox%7b%20for%20%7d1%5cleq%20i%3cj%5cleq%20n.%20%5c%5d%7d%25.png
    ( imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20S_X%20%5c%5d%7d%25.png is the set of elements of norme one of X and X* is the dual of X)

Reference

  • González, Manuel and Martínez-Abejón, Antonio,Supertauberian operators and perturbations., Arch. Math. 64, No.5, 423-433 (1995).