# Weak invertibility and strong spectrum

Studia Mathematica (1993)

- Volume: 105, Issue: 3, page 255-269
- ISSN: 0039-3223

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topMeyer, Michael. "Weak invertibility and strong spectrum." Studia Mathematica 105.3 (1993): 255-269. <http://eudml.org/doc/215998>.

@article{Meyer1993,

abstract = {A notion of weak invertibility in a unital associative algebra A and a corresponding notion of strong spectrum of an element of A is defined. It is shown that many relationships between the Jacobson radical, the group of invertibles and the spectrum have analogues relating the strong radical, the set of weakly invertible elements and the strong spectrum. The nonunital case is also discussed. A characterization is given of all (submultiplicative) norms on A in which every modular maximal ideal M ⊆ A is closed.},

author = {Meyer, Michael},

journal = {Studia Mathematica},

keywords = {radical; norm; spectrum; weak invertibility; strong spectrum; Jacobson radical; strong radical; modular maximal ideal},

language = {eng},

number = {3},

pages = {255-269},

title = {Weak invertibility and strong spectrum},

url = {http://eudml.org/doc/215998},

volume = {105},

year = {1993},

}

TY - JOUR

AU - Meyer, Michael

TI - Weak invertibility and strong spectrum

JO - Studia Mathematica

PY - 1993

VL - 105

IS - 3

SP - 255

EP - 269

AB - A notion of weak invertibility in a unital associative algebra A and a corresponding notion of strong spectrum of an element of A is defined. It is shown that many relationships between the Jacobson radical, the group of invertibles and the spectrum have analogues relating the strong radical, the set of weakly invertible elements and the strong spectrum. The nonunital case is also discussed. A characterization is given of all (submultiplicative) norms on A in which every modular maximal ideal M ⊆ A is closed.

LA - eng

KW - radical; norm; spectrum; weak invertibility; strong spectrum; Jacobson radical; strong radical; modular maximal ideal

UR - http://eudml.org/doc/215998

ER -

## References

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- [6] T. J. Ransford, Generalized spectra and analytic multivalued functions, J. London Math. Soc. (2) 29 (1984), 306-322. Zbl0508.46036
- [7] C. E. Rickart, On spectral permanence for certain Banach algebras, Proc. Amer. Math. Soc. 4 (1953), 191-196. Zbl0051.09106
- [8] C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, New York 1960.
- [9] L. B. Schweitzer, A nonspectral dense Banach subalgebra of the irrotational rotation algebra, preprint. Zbl0819.46053
- [10] A. M. Sinclair, Automatic Continuity of Linear Operators, London Math. Soc. Lecture Note Ser. 21, Cambridge Univ. Press, Cambridge 1976. Zbl0313.47029

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