Turkish Journal of Mathematics
Abstract
A bounded linear operator $T$ on a Hilbert space $\mathcal{H}$ is concave if, for each $x\in\mathcal{H}$, $\ T^2x\ ^2-2\ Tx\ ^2 +\ x\ ^2 \leq 0$. In this paper, it is shown that if $T$ is a concave operator then so is every power of $T$. Moreover, we investigate the concavity of shift operators. Furthermore, we obtain necessary and sufficient conditions for N-supercyclicity of co-concave operators. Finally, we establish necessary and sufficient conditions for the left and right multiplications to be concave on the Hilbert-Schmidt class.
DOI
10.3906/mat-1501-41
Keywords
Concave operators, weighted shifts, N-supercyclicity
First Page
1211
Last Page
1220
Recommended Citation
KARIMI, L, AHMADI, M. F, & HEDAYATIAN, K (2016). Some properties of concave operators. Turkish Journal of Mathematics 40 (6): 1211-1220. https://doi.org/10.3906/mat-1501-41
