On $(A,m)$-expansive operators
Volume 213 / 2012
Studia Mathematica 213 (2012), 3-23
MSC: Primary 47A63; Secondary 47A11.
DOI: 10.4064/sm213-1-2
Abstract
We give several conditions for $(A,m)$-expansive operators to have the single-valued extension property. We also provide some spectral properties of such operators. Moreover, we prove that the $A$-covariance of any $(A,2)$-expansive operator $T\in\mathcal{L(H)} $ is positive, showing that there exists a reducing subspace $\cal M$ on which $T$ is $(A,2)$-isometric. In addition, we verify that Weyl's theorem holds for an operator $T\in\mathcal{L(H)} $ provided that $T$ is $(T^{\ast}T,2)$-expansive. We next study $(A,m)$-isometric operators as a special case of $(A,m)$-expansive operators. Finally, we prove that every operator $T\in\mathcal{L(H)} $ which is $(T^{\ast}T,2)$-isometric has a scalar extension.
