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

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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 
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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. http://geodesic.mathdoc.fr/articles/10.4064/cm-67-2-289-295/

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