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On Banach modules I

Published online by Cambridge University Press:  24 October 2008

Sten Kaijser
Sten Kaijser
Affiliation:
Uppsala University
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Extract

The purpose of this series of papers is to present a general theory of Banach modules and to give some applications of it. The applications of the theory arise from observations that certain important notions of functional analysis are very closely related to certain Banach algebras and thereby to a module structure. This holds in particular for Banach lattices (which are C(X)-modules), interpolation spaces, tensor products and operator ideals.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 3 , November 1981 , pp. 423 - 444
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Arens, R.The adjoint of a bilinear operation. Proc. Amer. Math. Soc. 2 (1951), 836–849.CrossRefGoogle Scholar
(2)Arveson, W.An invitation to C*-algebras (Springer, Berlin-Heidelberg-New York, 1976).CrossRefGoogle Scholar
(3)Atzmon, A.Operators which are annihilated by analytic functions and invariant subspaces. Acta Math. 144 (1980), 27–63.CrossRefGoogle Scholar
(4)Beauzamy, B.Opérateurs uniformements convexifiants. Studia Math. LVII.Google Scholar
(5)Bergh, J. and Löfström, J.Interpolation spaces, an introduction (Springer, Berlin-Heidel-berg-New York, 1976).CrossRefGoogle Scholar
(6)Berkson, E. and Porta, H.Representations of F(X). J. Funct. Anal. 3 (1969), 1–34.CrossRefGoogle Scholar
(7)Brown, S., Chevreau, B. and Pearcy, C.Contractions with rich spectrum have invariant subspaces. J. Operator Theory 1 (1979), 123–136.Google Scholar
(8)Carne, T. K.Banach algebras and tensor products. J. London Math. Soc. 17 (1978), 480–488.CrossRefGoogle Scholar
(9)Carne, T. K.Not all H'-algebras are operator algebras.Math. Proc. Cambridge Philos. Soc. 86 (1979), 243–250.CrossRefGoogle Scholar
(10)Carne, T. K. Thesis, Cambridge 1978.Google Scholar
(11)Cigler, J., Losert, V. and Michor, P.Banach modules and functors on categories of Banach spaces (M. Dekker, New York, 1979).Google Scholar
(12)Cwikel, M.The dual of weak Lp. Ann. Inst. Fourier. 25 (1975), 81–126.CrossRefGoogle Scholar
(13)Davis, W., Figiel, T., Johnson, W. B. and Pelczynski, A.Factoring weakly compact operators. J. Funct. Anal. 7 (1974), 311–327.CrossRefGoogle Scholar
(14)Gillespie, T. A. Factorization in Banach function spaces (to appear).Google Scholar
(15)Grothendieck, A.Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Matem. Sao Paolo 8 (1956), 1–79.Google Scholar
(16)Harte, R. E. Tensor products of normed modules. Ph.D. Thesis, Cambridge 1964.Google Scholar
(17)Janson, S.On functions with conditions on the mean oscillation. Ark. Mat. 14 (1976), 189–196.CrossRefGoogle Scholar
(18)Kaijser, S.Local operators in Banach Lattices. Resulthate der Mathematik 2 (1979), no. 2, 151–170.Google Scholar
(19)Kaijser, S.Some representation theorems for Banach lattices. Ark. Mat. 16 (1978), 179–193.CrossRefGoogle Scholar
(20)Kaijser, S. On tensor products of Banach lattices (to appear in Monatshefte für Mathematik).Google Scholar
(21)Kaijser, S.A note on dual Banach spaces. Math. Scand. 41 (1977), 325–330.CrossRefGoogle Scholar
(22)Kaijser, S.A note on injective Banach algebras. Spaces of analytic functions (Kristiansand, Norway 1975, Springer Lecture Notes 512).Google Scholar
(23)Lindenstrauss, F. and Pelczynski, A.Absolutely summing operators in Lp–spaces and their applications. Studia Math. 29 (1968), 275–326.CrossRefGoogle Scholar
(24)Lorentz, G. G.Some new functional spaces. Ann. of Math. 51 (1950), 37–55.CrossRefGoogle Scholar
(25)Pietsch, A.Operator ideals (VEB Deutscher Verlag der Wissenchaften, Berlin, 1978).Google Scholar
(26)Pym, J. S.Convolution and the second dual of a Banach algebra. Proc. Cambridge Philos. Soc. 65 (1969), 597–599.CrossRefGoogle Scholar
(27)Schaefer, H. H.Banach lattices and positive operators (Springer, Berlin-Heidelberg-New York, 1974).CrossRefGoogle Scholar
(28)Tonge, A. Sur les algèbres de Banach et les opérateurs p–sommants (Séminaire Maurey-Schwartz 1975–1976).Google Scholar
(29)Varopoulos, N. Th.Sur les produits tensoriels des algèbres normées. C.R. Acad. Sci. Paris, Sér. A 276 (1973), 1193–1195.Google Scholar
(30)Varopoulos, N. Th. Sur les quotients des algèbres uniformes. C.R. Acad. Sci. Paris.Google Scholar
(31)Varopoulos, N. Th.A theorem on operator algebras. Math. Scand. 37 (1975), 173–182.CrossRefGoogle Scholar
(32)Wils, W.The ideal center of partially ordered vector spaces. Acta Math. 127 (1971), 41–77.CrossRefGoogle Scholar
(33)Young, N. J.Periodicity of functionals and representations of normed algebras on reflexive spaces. Proc. Edinburgh Math. Soc. 20 (1976), 99–120.CrossRefGoogle Scholar