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Metric generalizations of Banach algebras

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Rozprawy Matematyczne tom/nr w serii: 47 wydano: 1965
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CONTENTS
PRELIMINARIES
§ 0. Introduction.......................................................................................................................................................................3
§ 1. Definitions and notation.................................................................................................................................................5
Chapter I
LOCALLY 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...................................................................................................................................................................21
Chapter II
F-ALGEBRAS AND TOPOLOGICAL ALGEBRAS
§ 7. F-algebras.........................................................................................................................................................................23
§ 8. Topological division algebras.......................................................................................................................................26
Chapter III
$B_0$-ALGEBRAS
§ 9. Basic facts.........................................................................................................................................................................29
§ 10. Multiplicatively convex B_0-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.................................................................................................................................................................65
References...............................................................................................................................................................................68
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 47
Liczba stron
70
Liczba rozdzia³ów
Opis fizyczny
Rozprawy Matematyczne XLVII
Daty
wydano
1965
Twórcy
autor
  • Institute of Mathematics of the Polish Academy of Sciences and Yale University
Bibliografia
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  • [3] R. Arens, A generalization of normed rings, Pacific J. Math. 2 (1952), p. 465-471.
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  • [11] S. Mazur, Sur les anneaux linéaires, C. R. Acad. Sci. Paris 207 (1938), p. 1026-1027.
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  • [13] S. Mazur et W. Orlicz, Sur les espaces métriques linéaires (I), Studia Math. 10 (1948), p. 184-208.
  • [14] S. Mazur et W. Orlicz, Sur les espaces métriques linéaires (II), Studia Math. 13 (1953), p. 137-179.
  • [15] E. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952).
  • [16] Б. С. Митягин, Аппроксимативная размерность и базисы в ядерных пространствах, УМН 16, вып. 4 (100) (1961).
  • [17] B. Mitiagin, S. Rolewicz and W. Żelazko, Entire functions in B₀-algebras, Studia Math. 21 (1962), p. 291-306.
  • [18] М. А. Наймарк, Нормированные кольца, Москва 1956.
  • [19] C. E. Rickart, The uniqueness of norm problem, in Banach algebra, Ann. of Math. 51 (1950), p. 615-628.
  • [20] C. E. Rickart, General theory of Banach algebras, Princeton 1960.
  • [21] S. Rolewicz, On a certain class of linear metric spaces, Bull. Acad. Polon. Sc. 5 (1957), p. 479-484.
  • [22] S. Rolewicz, On spaces of holomorphic functions, Studia Math. 21 (1961), p. 135- 160.
  • [23] S. Rolewicz, Example of semi-simple m-convex B₀-algebra, which is not a projective limit of semi-simple B-algebras, Bull. Acad. Polon. Sc. II (1963), p. 459-462.
  • [24] S. Rolewicz, Entire functions in B₀-algebras containing dense division algebras, Studia Math. 23 (1963), p. 181-187.
  • [25] S. Rolewicz and W. Żelazko, Some problems concerning B₀-algebras, Tensor 13 (1963), p. 263-276.
  • [26] J. H. Williamson, On topologizing of the field C(t), Proc. Amer. Math. Soc. 5 (1954), p. 729-734.
  • [27] B. Yood, Ideals in topological rings, Canadian J. Math. 18 (1964), p. 28-45.
  • [28] W. Żelazko, On the locally bounded and m-convex topological algebras, Studia Math. 19 (1960), p. 333-356.
  • [29] W. Żelazko, On the radicals of p-normed algebras, Studia Math. 21 (1962), p. 203-206.
  • [30] W. Żelazko, Analytic functions in p-normed algebras, Studia Math. 21 (1962), p. 345-350.
  • [31] W. Żelazko, On decomposition of a commutative p-normed algebra into a direct sum of ideals, Coll. Math. 10 (1963), p. 57-60.
  • [32] W. Żelazko, A theorem on B₀ division algebras, Bull. Acad. Pol. Sc. 8 (1960), p. 373-375.
  • [33] W. Żelazko, A theorem on discrete groups and algebras $L_p$, Coll. Math. 8 (1961), p. 205-207.
  • [34] D. Przeworska-Rolewicz and S. Rolewicz, On integrals of functions with values in a linearly metric complete space, Studia Math. 26 (1965).
  • [35] I. E. Littlewood, Lectures on theory of functions, London 1944.
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