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1
Content available remote

On rank one elements

100%
Harte R.
Studia Mathematica
|
1995-1996
|
tom 117
|
nr 1
73-77
XX
Without the "scarcity lemma", two kinds of "rank one elements" are identified in semisimple Banach algebras.
2
Content available remote

On Kato non-singularity

100%
Harte R.
Studia Mathematica
|
1995-1996
|
tom 117
|
nr 2
107-114
EN
An exactness lemma offers a simplified account of the spectral properties of the "holomorphic" analogue of normal solvability.
3
Content available remote

Correction to "An index formula for chains" (Studia Math. 116 (1995), 283-294)

64%
Harte R., Lee W. Y.
Studia Mathematica
|
1996
|
tom 118
|
nr 3
305
4
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The spectral topology in rings

64%
Cvetković-Ilić D., Harte R.
Studia Mathematica
|
2010
|
tom 200
|
nr 3
267-278
EN
The spectral topology of a ring is easily defined, has familiar applications in elementary Banach algebra theory, and appears relevant to abstract Fredholm and stable range theory.
5
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An index formula for chains

64%
Harte R., Lee W. Y.
Studia Mathematica
|
1995
|
tom 116
|
nr 3
283-294
EN
We derive a formula for the index of Fredholm chains on normed spaces.
6
Content available remote

Almost exactness in normed spaces II

64%
Harte R., Мbekhta M.
Studia Mathematica
|
1995-1996
|
tom 117
|
nr 2
101-105
EN
In the normed space of bounded operators between a pair of normed spaces, the set of operators which are "bounded below" forms the interior of the set of one-one operators. This note is concerned with the extension of this observation to certain spaces of pairs of operators.
7
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On generalized inverses in C*-algebras

64%
Harte R., Mbekhta M.
Studia Mathematica
|
1992
|
tom 103
|
nr 1
71-77
EN
We investigate when a C*-algebra element generates a closed ideal, and discuss Moore-Penrose and commuting generalized inverses.
8
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The closure of the invertibles in a von Neumann algebra

64%
Burlando L., Harte R.
Colloquium Mathematicum
|
1996
|
tom 69
|
nr 2
157-165
EN
In this paper we consider a subset  of a Banach algebra A (containing all elements of A which have a generalized inverse) and characterize membership in the closure of the invertibles for the elements of Â. Thus our result yields a characterization of the closure of the invertible group for all those Banach algebras A which satisfy  = A. In particular, we prove that  = A when A is a von Neumann algebra. We also derive from our characterization new proofs of previously known results, namely Feldman and Kadison's characterization of the closure of the invertibles in a von Neumann algebra and a more recent characterization of the closure of the invertibles in the bounded linear operators on a Hilbert space.
9
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Generalized inverses in C*-algebras II

64%
Harte R., Mbekhta M.
Studia Mathematica
|
1993
|
tom 106
|
nr 2
129-138
EN
Commutativity and continuity conditions for the Moore-Penrose inverse and the "conorm" are established in a C*-algebra; moreover, spectral permanence and B*-properties for the conorm are proved.
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