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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Topological spectrum of elements in topological algebras; pp. 271–281

(Full article in PDF format) https://doi.org/10.3176/proc.2018.3.05


Authors

Mati Abel, Yuliana de Jesús Zárate-Rodríguez

Abstract

Properties of the sets of left, right, and two-sided topologically quasi-invertible elements, topological spectra, and topological spectral radii of elements in (not necessarily unital or commutative) topological algebras are studied. We prove the spectral mapping theorem for the topological spectrum of elements in commutative complex (not necessarily unital) topological algebras and show that the topological spectral radius (as a map) is a submultiplicative seminorm in a topological algebra with a functional topological spectrum.

Keywords

topological algebra, topological spectrum of an element, F-algebra, continuity of quasi-invertion, functional topological spectrum.

References

1. Abel , M. Advertive topological algebras. In General Topological Algebras. Proceedings of the International Workshop , Tartu , 4–7 October , 1999; Math. Stud. (Tartu) , 2001 , 1 , 14–24.

2. Abel , M. and ˙ Zelazko , W. Topologically invertible elements and the topological spectrum. Bull. Pol. Acad. Sci. Math. , 2006 , 54 , 257–271.
https://doi.org/10.4064/ba54-3-7

3. Abel , M. , Palacios , L. , and Zárate , Y. On TQ-algebras. Mediterr. J. Math. , 2017 , 14(5) , 14:184.

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5. Choukri , R. and El Kinani , A. Topological algebras with ascending or descending chain condition. Arch. Math. (Basel) , 1999 , 72 , 438–443.
https://doi.org/10.1007/s000130050353

6. Fragoulopoulou , M. Topological Algebras with Involution. North-Holland Mathematics Studies , 200. Elsevier Science B.V. , Amsterdam , 2005.

7. Najmi , A. Topologically Q-algebras. Bull. Greek Math. Soc. , 2009 , 560 , 29–45.

8. Waelbroeck , L. Topological Vector Spaces and Algebras. Lecture Notes in Mathematics , 230. Springer-Verlag , Berlin , 1973.

9. Warner , S. Topological Fields. North-Holland Mathematics Studies , 157. Noth-Holland Publishing Company , Amsterdam , 1989.

 
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Current Issue: Vol. 69, Issue 2, 2020




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
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