Summary
In the paper we prove two inequalities involving Gelfand numbers of operators with values in a Hilbert space. The first inequality is a Rademacher version of the main result in [Pa-To-1] which relates the Gelfand numbers of an operator from a Banach spaceX intol n2 with a certain Rademacher average for the dual operator. The second inequality states that the Gelfand numbers of an operatoru froml N1 into a Hilbert space satisfy the inequality
whereC is a universal constant. Several applications of these inequalities in the geometry of Banach spaces are given.
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Carl, B., Pajor, A. Gelfand numbers of operators with values in a Hilbert space. Invent Math 94, 479–504 (1988). https://doi.org/10.1007/BF01394273
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DOI: https://doi.org/10.1007/BF01394273