Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 30, Tome 290 (2002), pp. 27-32
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M. F. Gamal'. Lattcies of invariant subspaces for a quasiaffine transform of a unilateral shift of finite multiplicity. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 30, Tome 290 (2002), pp. 27-32. http://geodesic.mathdoc.fr/item/ZNSL_2002_290_a1/
@article{ZNSL_2002_290_a1,
author = {M. F. Gamal'},
title = {Lattcies of invariant subspaces for a quasiaffine transform of a unilateral shift of finite multiplicity},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {27--32},
year = {2002},
volume = {290},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_290_a1/}
}
TY - JOUR
AU - M. F. Gamal'
TI - Lattcies of invariant subspaces for a quasiaffine transform of a unilateral shift of finite multiplicity
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2002
SP - 27
EP - 32
VL - 290
UR - http://geodesic.mathdoc.fr/item/ZNSL_2002_290_a1/
LA - ru
ID - ZNSL_2002_290_a1
ER -
%0 Journal Article
%A M. F. Gamal'
%T Lattcies of invariant subspaces for a quasiaffine transform of a unilateral shift of finite multiplicity
%J Zapiski Nauchnykh Seminarov POMI
%D 2002
%P 27-32
%V 290
%U http://geodesic.mathdoc.fr/item/ZNSL_2002_290_a1/
%G ru
%F ZNSL_2002_290_a1
Let $T$ be a contraction, let $S$ be an unilateral shift of finite multiplicity, and let $X$ be an operator with zero kernel, dense range, and such that $XT=SX$. Then the mapping $E\mapsto\text{clos}XE$, $E\in\text{Lat}T$, is an isomorphism between the latticies $\text{Lat}T$ and $\text{Lat}S$ of invariant subspaces of $T$ and $S$.
