The 2-summing norm of l<sup>n</sup><sub>p</sub> computed with n vectors


Abstract


The 2-summing norm of an n-dimensional Banach space computed with n vectors is known to belong between n<sup>1/2</sup>/√{2} and n<sup>1/2</sup>. It is shown that the 2-summing norm of real l<sub>1</sub><sup>3</sup> computed with three vectors is 5/3. Some lower estimates for 2-summing norms of l<sub>p</sub><sup>n</sup> computed with n vectors are stated, which are considerably better than universal ones and are based on the existence of certain block designs or Hadamard matrices.

DOI Code: 10.1285/i15900932v14n1p81

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