Extension constants of unconditional two-dimensional operators. (English) Zbl 0851.15019
Summary: It is shown that the (absolute) extension constant \(e(T)\) of an operator \(T\) such that \(Tv_k= \lambda_k v_k\), \(k= 1, 2\), for some unconditional basis \((v_1, v_2)\) of a two-dimensional real normed space is less than or equal to \((|\lambda_1 |+ |\lambda_2|+ 2\sqrt {\lambda^2_1- |\lambda_1 \lambda_2 |+ \lambda^2_2} )/3\). In fact, it is demonstrated that \(e(T)\) is attained by exactly one unconditional two-dimensional space (up to an isometry).
MSC:
| 15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |
References:
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