English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

An operator $T$ on a Hilbert space $\mathcal H$ is called expansive, if$\|Tx\|\geq \|x\|$ ($x\in\mathcal H$). Expansive operators $T$ quasisimilar tothe unilateral shift $S_N$ of finite multiplicity $N$ are studied. It is provedthat $I-T^*T$ is of trace class for such $T$. Also the lattice $\mathrm{Lat}T$of invariant subspaces of an expansive operator $T$ quasisimilar to $S_N$ isstudied. It is proved that $\dim\mathcal M\ominus T\mathcal M\leq N$ for every$\mathcal M\in\mathrm{Lat}T$. It is shown that if $N\geq 2$, then there exist$\mathcal M_j\in\mathrm{Lat}T$ ($j=1,\ldots, N$) such that the restriction$T|_{\mathcal M_j}$ of $T$ on $\mathcal M_j$ is similar to the unilateral shift$S$ of multiplicity $1$ for every $j=1,\ldots, N$, and $\mathcalH=\vee_{j=1}^N\mathcal M_j$. For $N=1$, that is, for $T$ quasisimilar to $S$,there exist two spaces $\mathcal M_1$, $\mathcal M_2\in\mathrm{Lat}T$ such that$T|_{\mathcal M_j}$ is similar to $S$ for $j=1,2$, and $\mathcal H=\mathcalM_1\vee\mathcal M_2$. Example of an expansive operator $T$ quasisimilar to $S$is given such that intertwining transformations do not give an isomorphism of$\mathrm{Lat}T$ and $\mathrm{Lat}S$.

On expansive operators that are quasisimilar to the unilateral shift of finite multiplicity