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Turkish Journal of Mathematics

DOI

10.3906/mat-1501-41

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.

First Page

1211

Last Page

1220

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