Topics in Banach space theory

Tensor products of vector spaces - bilinear forms, tensors as linear mappings, tensor and trace duality.

The projective tensor product - the projective norm, the dual space.

The injective tensor product - the injective norm, C(K) and L - infinity spaces.

The Chevet Saphar tensor norms, The Hilbertian tensor norm.

The minimal tensor product, Ruan’s theorem, basics of operator space theory.

Prerequisite courses: Analysis II (Measure Theory), Functional Analysis.

References:

  1. Banach algebras and automatic continuity by Harold Garth Dales, London Mathematical Society Monographs. New Series, 24.<http://www.ams.org/mathscinet/search/ series.html?cn=London_Mathematical_Society_Monographs_New_Series>Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 2000.

  2. Introduction to Operator Space Theory by Gilles Pisier, London Mathematical Society Lecture Note Series 294, Cambridge University Press 2003.

  3. Introduction to Tensor Products of Banach Spaces by Raymond A. Ryan, Springer Monographs in Mathematics, Springer Verlag 2001

 


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Last updated: 31 May 2023