Norm attainment set and symmetricity of operators on l(p)(2)

摘要

We study the norm attainment set and the minimum norm attainment set of an operator defined on l(p)(2)(R) (1 < p < infinity). We obtain a complete description of the same from the point of view of cardinality. In particular, we establish the optimal bounds in both the cases. Whenever the operator is not a scalar multiple of an isometry, the upper bound is 4. Moreover, we obtain an upper bound for the norm of an operator on l(p)(2)(R) (1 < p < infinity). We further prove that there is no non-zero left symmetric operator on l(p)(2)(C)(2 <= p < infinity).