Extension constants of unconditional two-dimensional operators Original Research Article

It is shown that the (absolute) extension constant e(T) of an operator T such that Tvk = λkvk, K = 1, 2, for some unconditional basis (v1, v2) of a two-dimensional real normed space is less than or equal to λ1 + λ2 + 2√λ21 − λ1λ2 + λ22)/3. In fact, it is demonstrated that e(T) is attained by exactly one unconditional two-dimensional space (up to an isometry).