Methods in the theory of hereditarily indecomposable Banach spaces

2004 ◽  
Vol 170 (806) ◽  
pp. 0-0 ◽  
Author(s):  
Spiros A. Argyros ◽  
Andreas Tolias
Keyword(s):  
Banach Spaces ◽  
Hereditarily Indecomposable Banach Spaces ◽  
Hereditarily Indecomposable

scholarly journals On hereditarily indecomposable Banach spaces

2004 ◽  
Vol 126 (1-3) ◽  
pp. 293-299 ◽  
Author(s):  
Tadeusz Figiel ◽  
Ryszard Frankiewicz ◽  
Ryszard Komorowski ◽  
Czesław Ryll-Nardzewski
Keyword(s):  
Banach Spaces ◽  
Hereditarily Indecomposable Banach Spaces ◽  
Hereditarily Indecomposable

scholarly journals Quotient Hereditarily Indecomposable Banach Spaces

1999 ◽  
Vol 51 (3) ◽  
pp. 566-584 ◽  
Author(s):  
V. Ferenczi
Keyword(s):  
Banach Space ◽  
Singular Perturbation ◽  
Banach Spaces ◽  
Infinite Dimensional ◽  
Strictly Singular ◽  
Hereditarily Indecomposable Banach Spaces ◽  
Hereditarily Indecomposable

AbstractA Banach space X is said to be quotient hereditarily indecomposable if no infinite dimensional quotient of a subspace of X is decomposable. We provide an example of a quotient hereditarily indecomposable space, namely the space XGM constructed by W. T. Gowers and B. Maurey in [GM]. Then we provide an example of a reflexive hereditarily indecomposable space whose dual is not hereditarily indecomposable; so is not quotient hereditarily indecomposable. We also show that every operator on * is a strictly singular perturbation of an homothetic map.

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