Some properties of concave operators

Authors

LOTFOLLAH KARIMI
MASOUMEH FAGHIH AHMADI
KARIM HEDAYATIAN

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.

Keywords

Concave operators, weighted shifts, N-supercyclicity

First Page

1211

Last Page

1220

Recommended Citation

KARIMI, LOTFOLLAH; AHMADI, MASOUMEH FAGHIH; and HEDAYATIAN, KARIM (2016) "Some properties of concave operators," Turkish Journal of Mathematics: Vol. 40: No. 6, Article 3. https://doi.org/10.3906/mat-1501-41
Available at: https://journals.tubitak.gov.tr/math/vol40/iss6/3