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The structure of the closed linear span of the Rademacher functions in the Cesàro space is investigated. It is shown that every infinite-dimensional subspace of either is isomorphic to l₂ and uncomplemented in , or contains a subspace isomorphic to c₀ and complemented in . The situation is rather different in the p-convexification of if 1 < p < ∞.
Sergey V. Astashkin, and Lech Maligranda. "Structure of Rademacher subspaces in Cesàro type spaces." Studia Mathematica 226.3 (2015): 259-279. <http://eudml.org/doc/285407>.
@article{SergeyV2015, abstract = {The structure of the closed linear span of the Rademacher functions in the Cesàro space $Ces_\{∞\}$ is investigated. It is shown that every infinite-dimensional subspace of either is isomorphic to l₂ and uncomplemented in $Ces_\{∞\}$, or contains a subspace isomorphic to c₀ and complemented in . The situation is rather different in the p-convexification of $Ces_\{∞\} $ if 1 < p < ∞.}, author = {Sergey V. Astashkin, Lech Maligranda}, journal = {Studia Mathematica}, keywords = {Rademacher functions; Cesàro function spac; Korenblyum-Krein-Levin space; subspaces; complemented subspaces}, language = {eng}, number = {3}, pages = {259-279}, title = {Structure of Rademacher subspaces in Cesàro type spaces}, url = {http://eudml.org/doc/285407}, volume = {226}, year = {2015}, }
TY - JOUR AU - Sergey V. Astashkin AU - Lech Maligranda TI - Structure of Rademacher subspaces in Cesàro type spaces JO - Studia Mathematica PY - 2015 VL - 226 IS - 3 SP - 259 EP - 279 AB - The structure of the closed linear span of the Rademacher functions in the Cesàro space $Ces_{∞}$ is investigated. It is shown that every infinite-dimensional subspace of either is isomorphic to l₂ and uncomplemented in $Ces_{∞}$, or contains a subspace isomorphic to c₀ and complemented in . The situation is rather different in the p-convexification of $Ces_{∞} $ if 1 < p < ∞. LA - eng KW - Rademacher functions; Cesàro function spac; Korenblyum-Krein-Levin space; subspaces; complemented subspaces UR - http://eudml.org/doc/285407 ER -