Geodesic
On strongly closed subalgebras of B(X)
Colloquium Mathematicum, Tome 67 (1994) no. 2, pp. 289-295

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let X be a real or complex Banach space. The strong topology on the algebra B(X) of all bounded linear operators on X is the topology of pointwise convergence of nets of operators. It is given by a basis of neighbourhoods of the origin consisting of sets of the form (1) U(ε;x_{1},...,x_{n}) = {T ∈ B(X): ∥ Tx_{i}∥ , i=1,...,n},$ where $x_{1},...,x_{n}$ are linearly independent elements of X and ε is a positive real number. Closure in the strong topology will be called strong closure for short. It is well known that the strong closure of a subalgebra of B(X) is again a subalgebra. In this paper we study strongly closed subalgebras of B(X), in particular, maximal strongly closed subalgebras. Our results are given in Section 1, while in Section 2 we give the motivation for this study and pose several open questions.
DOI : 10.4064/cm-67-2-289-295

W. Żelazko 1

1 
@article{10_4064_cm_67_2_289_295,
     author = {W. \.Zelazko},
     title = {On strongly closed subalgebras of {B(X)}},
     journal = {Colloquium Mathematicum},
     pages = {289--295},
     publisher = {mathdoc},
     volume = {67},
     number = {2},
     year = {1994},
     doi = {10.4064/cm-67-2-289-295},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-67-2-289-295/}
}
TY  - JOUR
AU  - W. Żelazko
TI  - On strongly closed subalgebras of B(X)
JO  - Colloquium Mathematicum
PY  - 1994
SP  - 289
EP  - 295
VL  - 67
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-67-2-289-295/
DO  - 10.4064/cm-67-2-289-295
LA  - en
ID  - 10_4064_cm_67_2_289_295
ER  - 
%0 Journal Article
%A W. Żelazko
%T On strongly closed subalgebras of B(X)
%J Colloquium Mathematicum
%D 1994
%P 289-295
%V 67
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-67-2-289-295/
%R 10.4064/cm-67-2-289-295
%G en
%F 10_4064_cm_67_2_289_295
W. Żelazko. On strongly closed subalgebras of B(X). Colloquium Mathematicum, Tome 67 (1994) no. 2, pp. 289-295. doi: 10.4064/cm-67-2-289-295

Cité par Sources :