Abstract
We define the basic concepts of the theory of M-structure and investigate the M-structure properties of the ∈-tensor product. Our main result generalizes a theorem due to author. It describes how the centralizer of the tensor product can be constructed from the centralizers of the factors. In the last sections we investigate some applications and indicate some open problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alfsen-Effros, E.M., M-structure in real Banach spaces I/II Ann. of Math. 96 (1972), 78–173.
Archbold, R.J., On the centre of a tensor product of C*-algebras J. of the Ldn. Math. Soc. 10 (1975), 257–262.
Batty, C.J., Tensor products of compact convex sets and Banach algebras, Math. Proc. Camb. Phil. Soc. 83 (1978), 419–427.
Behrends, E., The centralizer of tensor products of Banach spaces, Pacific Journal of Math. (to appear, 1979).
Behrends, E., An application of M-structure to theorems of the Banach-Stone type, in: Notas de Mathematica, Math. Studies 27 (1977), 29–49.
Behrends, E.-Schmidt-Bichler, U., M-structure and the Banach-Stone theorem, Studia Math. 68 (1979) (to appear)
Chui, C.K. et al., L-ideals and numerical range preservation, Ill. J. of Math. 21 (1977), 365–373.
Cunningham, F., M-structure in Banach spaces, Proc. of the Ca Camb. Phil. Soc. 63 (1967), 613–629.
Cunningham, F.-Roy, N.M., Extreme functionals on an upper semicontinuous function space, Proc. of the American Math. Soc. 42 (1974), 461–465.
Haydon, R.G.-Wassermann, A.S., A commutation result for tensor products of C*-algebras, Bull. Ldn. Math. Soc. 5 (1973), 283–287.
Holmes, R. et al., Best approximation by compact operators, Bull. of the AMS 80 (1974), 98–102.
Vincent-Smith, G.F., The centre of the tensor product of AK-spaces, Quart. J. Math. Oxford 28 (1977), 87–91.
Wickstead, A.W., The centralizer of E⊗λ F, Pac. J. of Math. 65 (1976), 563–571.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Behrends, E. (1981). M-structure in tensor products of Banach spaces. In: Machado, S. (eds) Functional Analysis, Holomorphy, and Approximation Theory. Lecture Notes in Mathematics, vol 843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089269
Download citation
DOI: https://doi.org/10.1007/BFb0089269
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10560-2
Online ISBN: 978-3-540-38529-5
eBook Packages: Springer Book Archive