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We introduce and investigate a class of non-separable tree-like Banach spaces. As a consequence, we prove that we cannot achieve a satisfactory extension of Rosenthal's ℓ₁-theorem to spaces of the type ℓ₁(κ) for κ an uncountable cardinal.
Costas Poulios. "Non-separable tree-like Banach spaces and Rosenthal's ℓ₁-theorem." Studia Mathematica 221.1 (2014): 1-12. <http://eudml.org/doc/285598>.
@article{CostasPoulios2014, abstract = {We introduce and investigate a class of non-separable tree-like Banach spaces. As a consequence, we prove that we cannot achieve a satisfactory extension of Rosenthal's ℓ₁-theorem to spaces of the type ℓ₁(κ) for κ an uncountable cardinal.}, author = {Costas Poulios}, journal = {Studia Mathematica}, keywords = {non-separable tree-like Banach spaces; Rosenthal’s -theorem; uncountable cardinal}, language = {eng}, number = {1}, pages = {1-12}, title = {Non-separable tree-like Banach spaces and Rosenthal's ℓ₁-theorem}, url = {http://eudml.org/doc/285598}, volume = {221}, year = {2014}, }
TY - JOUR AU - Costas Poulios TI - Non-separable tree-like Banach spaces and Rosenthal's ℓ₁-theorem JO - Studia Mathematica PY - 2014 VL - 221 IS - 1 SP - 1 EP - 12 AB - We introduce and investigate a class of non-separable tree-like Banach spaces. As a consequence, we prove that we cannot achieve a satisfactory extension of Rosenthal's ℓ₁-theorem to spaces of the type ℓ₁(κ) for κ an uncountable cardinal. LA - eng KW - non-separable tree-like Banach spaces; Rosenthal’s -theorem; uncountable cardinal UR - http://eudml.org/doc/285598 ER -