Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 23-56
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V. V. Kapustin; A. V. Lipin. Operator algebras and invariant subspaces lattices. I. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 23-56. http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a1/
@article{ZNSL_1989_178_a1,
author = {V. V. Kapustin and A. V. Lipin},
title = {Operator algebras and invariant subspaces {lattices.~I}},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {23--56},
year = {1989},
volume = {178},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a1/}
}
TY - JOUR
AU - V. V. Kapustin
AU - A. V. Lipin
TI - Operator algebras and invariant subspaces lattices. I
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1989
SP - 23
EP - 56
VL - 178
UR - http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a1/
LA - ru
ID - ZNSL_1989_178_a1
ER -
%0 Journal Article
%A V. V. Kapustin
%A A. V. Lipin
%T Operator algebras and invariant subspaces lattices. I
%J Zapiski Nauchnykh Seminarov POMI
%D 1989
%P 23-56
%V 178
%U http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a1/
%G ru
%F ZNSL_1989_178_a1
Given a bounded linear operator $T$, we study the following questions: when the commutant $\{T\}'$ is commutative; when each operator in the bicomrautant $\{T\}''$ can be approximated by polynomials of $T$ in the weak operator topology, the problem of reflexivity and others. These questions are solved for some classes of operators.
