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We describe how the Szlenk index has been used in various areas of the geometry of Banach spaces. We cover the following domains of application of this notion: non existence of universal spaces, linear classification of C(K) spaces, descriptive set theory, renorming problems and non linear classification of Banach spaces.
Lancien, Gilles. "A survey on the Szlenk index and some of its applications.." RACSAM 100.1-2 (2006): 209-235. <http://eudml.org/doc/41653>.
@article{Lancien2006, abstract = {We describe how the Szlenk index has been used in various areas of the geometry of Banach spaces. We cover the following domains of application of this notion: non existence of universal spaces, linear classification of C(K) spaces, descriptive set theory, renorming problems and non linear classification of Banach spaces.}, author = {Lancien, Gilles}, journal = {RACSAM}, keywords = {dentability; renorming; analysis sets; Kadec-Klee norm; LUR norm; descriptive set theory}, language = {eng}, number = {1-2}, pages = {209-235}, title = {A survey on the Szlenk index and some of its applications.}, url = {http://eudml.org/doc/41653}, volume = {100}, year = {2006}, }
TY - JOUR AU - Lancien, Gilles TI - A survey on the Szlenk index and some of its applications. JO - RACSAM PY - 2006 VL - 100 IS - 1-2 SP - 209 EP - 235 AB - We describe how the Szlenk index has been used in various areas of the geometry of Banach spaces. We cover the following domains of application of this notion: non existence of universal spaces, linear classification of C(K) spaces, descriptive set theory, renorming problems and non linear classification of Banach spaces. LA - eng KW - dentability; renorming; analysis sets; Kadec-Klee norm; LUR norm; descriptive set theory UR - http://eudml.org/doc/41653 ER -