# Topologies on the space of ideals of a Banach algebra

Studia Mathematica (1995)

- Volume: 115, Issue: 2, page 189-205
- ISSN: 0039-3223

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topBeckhoff, Ferdinand. "Topologies on the space of ideals of a Banach algebra." Studia Mathematica 115.2 (1995): 189-205. <http://eudml.org/doc/216207>.

@article{Beckhoff1995,

abstract = {Some topologies on the space Id(A) of two-sided and closed ideals of a Banach algebra are introduced and investigated. One of the topologies, namely $τ_∞$, coincides with the so-called strong topology if A is a C*-algebra. We prove that for a separable Banach algebra $τ_∞$ coincides with a weaker topology when restricted to the space Min-Primal(A) of minimal closed primal ideals and that Min-Primal(A) is a Polish space if $τ_∞$ is Hausdorff; this generalizes results from [1] and [5]. All subspaces of Id(A) with the relative hull kernel topology turn out to be separable Lindelöf spaces if A is separable, which improves results from [14].},

author = {Beckhoff, Ferdinand},

journal = {Studia Mathematica},

keywords = {space of two-sided and closed ideals of a Banach algebra; minimal closed primal ideals; Polish space; separable Lindelöf spaces},

language = {eng},

number = {2},

pages = {189-205},

title = {Topologies on the space of ideals of a Banach algebra},

url = {http://eudml.org/doc/216207},

volume = {115},

year = {1995},

}

TY - JOUR

AU - Beckhoff, Ferdinand

TI - Topologies on the space of ideals of a Banach algebra

JO - Studia Mathematica

PY - 1995

VL - 115

IS - 2

SP - 189

EP - 205

AB - Some topologies on the space Id(A) of two-sided and closed ideals of a Banach algebra are introduced and investigated. One of the topologies, namely $τ_∞$, coincides with the so-called strong topology if A is a C*-algebra. We prove that for a separable Banach algebra $τ_∞$ coincides with a weaker topology when restricted to the space Min-Primal(A) of minimal closed primal ideals and that Min-Primal(A) is a Polish space if $τ_∞$ is Hausdorff; this generalizes results from [1] and [5]. All subspaces of Id(A) with the relative hull kernel topology turn out to be separable Lindelöf spaces if A is separable, which improves results from [14].

LA - eng

KW - space of two-sided and closed ideals of a Banach algebra; minimal closed primal ideals; Polish space; separable Lindelöf spaces

UR - http://eudml.org/doc/216207

ER -

## References

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- [9] R. S. Doran and V. A. Belfi, Characterizations of C*-algebras, Marcel Dekker, 1986. Zbl0597.46056
- [10] R. A. Hirschfeld and W. Żelazko, On spectral norm Banach algebras, Bull. Acad. Polon. Sci. 16 (1968), 195-199. Zbl0159.18403
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- [13] S. Sakai, C*-algebras and W*-algebras, Springer, 1971.
- [14] D. W. B. Somerset, Minimal primal ideals in Banach algebras, Math. Proc. Cambridge Philos. Soc. 115 (1994), 39-52.
- [15] A. Wilansky, Between ${T}_{1}$ and ${T}_{2}$, Amer. Math. Monthly 74 (1967), 261-266.

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