Metric generalizations of Banach algebras

W. Żelazko

GDML_Books, (1965), p.

Résumé

CONTENTSPRELIMINARIES§ 0. Introduction.......................................................................................................................................................................3§ 1. Definitions and notation.................................................................................................................................................5Chapter ILOCALLY BOUNDED ALGEBRAS§ 2. Basic facts and examples..............................................................................................................................................6§ 3. Commutative p-normed algebras, spectral form and p-normed field..................................................................8§ 4. Commutative p-normed algebras (continued)..........................................................................................................12§ 5. Analytic functions in p-normed algebras.....................................................................................................................16§ 6. Final remarks...................................................................................................................................................................21Chapter IIF-ALGEBRAS AND TOPOLOGICAL ALGEBRAS§ 7. F-algebras.........................................................................................................................................................................23§ 8. Topological division algebras.......................................................................................................................................26Chapter III$B_0$-ALGEBRAS§ 9. Basic facts.........................................................................................................................................................................29§ 10. Multiplicatively convex B0-algebras.........................................................................................................................31§ 11. Spectra and power series in commutative m-convex $B_0$-algebras..............................................................34§ 12. Examples of non-m-convex $B_0$-algebras..........................................................................................................40§ 13. Extended spectrum; theorem on entire functions and its applications to Q-algebras and radicals.............44§ 14. Elementary properties of entire functions and characterization of commutative $B_0$-algebras with and without entire functions..................................................................................................................................................51§ 15. Entire operations in $B_0$-spaces and their applications to entire functions.................................................56§ 16. Final remarks.................................................................................................................................................................65References...............................................................................................................................................................................68

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Zbl 0131.13005

EUDML-ID : urn:eudml:doc:268341