The set of supporting vectors of a continuous linear operator \(T:X\rightarrow Y\) between normed spaces, denoted by \(\mathrm {suppv}(T)\) since 2017, is defined as \(\mathrm {suppv}(T):=\{x\in X:\Vert T(x)\Vert =\Vert T\Vert \Vert x\Vert \}\). In this manuscript, we study the lineability and coneability properties of \(\mathrm {suppv}(T)\), reaching both positive and negative results depending on T. For instance, if T is a functional, then \(\mathrm {suppv}(T)\) is 1-lineable and this result cannot be improved. However, if T is a (1, 1)-projection and X is infinite dimensional, then either \(\mathrm {suppv}(T)\) or \(\mathrm {suppv}(I-T)\) is lineable. Other general sufficient conditions for \(\mathrm {suppv}(T)\) to be lineable and coneable are provided. Special attention is given to the case where X and Y are Hilbert spaces, obtaining a characterization of unitary operators. The particular case of operators on \(\ell _1\) and \(c_0\) is also studied.

自2017年以来以\（\ mathrm {suppv}（T）\）表示的规范空间之间的连续线性算子\（T：X \ rightarrow Y \）的支持向量集定义为\（\ mathrm {suppv }（T）：= \ {x \ in X：\ Vert T（x）\ Vert = \ Vert T \ Vert \ Vert x \ Vert \} \）。在本手稿中，我们研究\（\ mathrm {suppv}（T）\）的可线性性和圆锥性，根据T达到正和负结果。例如，如果T是一个函数，则\（\ mathrm {suppv}（T）\）是1线的，此结果无法改善。但是，如果T是（1，1）投影而X是无限维，则\（\ mathrm {suppv}（T）\）或\（\ mathrm {suppv}（IT）\）是可排列的。为\（\ mathrm {suppv}（T）\）提供可线化和可锥化的其他一般充分条件。特别注意X和Y是希尔伯特空间的情况，获得obtaining算子的特征。还研究了\（\ ell _1 \）和\（c_0 \）上运算符的特殊情况。